I'm purely basing this on my experiences from Objective Mode, the majority of my matches have been played on Nightmare Difficulty.
Just to preface, I am not some god gamer but I generally succeed on my Nightmare rounds. This is less about 'buff this' or 'nerf that' and more what should probably be either be discussed and picked upon by the community or potentially integrated into the base kit for responders and/or reworked alongside it. I'm not going to mention every perk, just the ones I think need mentioning. My personal rework suggestions if I have any will be in italics.
tl;dr - perk feedback yap
Must-haves.
Athlete - Stamina in this game is real important. Every responder I have, has this perk. The expert version lets you kick twice without running out of stamina which is pretty big. More stamina = more attacks, more shoves and more sprinting time especially when paired up with Marathon Runner. I think the game would be a lot healthier if stamina costs across the board were reworked, or they simply just slap Athlete into the base responder parameters instead and then balance the game around that from there. If do that, they could rework Athlete into boosting the distance of zombies being staggered/pushed over by attacks, shoves and kicks maybe.
Marathon Runner - This perk is really desirable, especially on the bigger maps like Power Plant, Lewiston and Pottsville. More time sprinting means further distances covered in a shorter amount of time which can really add up on time saved otherwise travelling, especially on Power Plant. Personally I'd just make the expert version baked into the base parameters of Responders and change the effects of this perk to improve stamina regeneration whilst moving when not sprinting.
Really good ones, most of the time 99% of the times.
Sturdy Body - 10%/20% less damage taken, if running normal/expert and this stacks ontop of Body Armor. Couple this with Thick Skin and you'll get tons of mileage. On it's own with expert this turns prime zombie hits (25) down to normal zombie hits (20) and normal zombie hits drop down to 16 per hit.
Thick Skin - More health is always good. Couple it with Sturdy Body for maximum mileage to soak more hits than someone without. This and Sturdy Body aren't perks you really need to have, thanks to shoving and kicking giving iframes, but they're never a bad option and they're 100% worth having no matter the build to keep you above the 50% HP threshold to avoid infection chances on swipes.
Hitman - If you're running one handed melee weapons, this is big one if you want to increase the speed in which you kill zombies as well as actually save on stamina despite attacks costing more. For example, the Cleaver goes from 2 charged attacks to the head to kill a normal zombie to 1 charged attack and 1 light attack, spending only 21 Stamina instead of 26.
Rush - Reduces Stamina on 2 Handed Melee Charged attacks. If you're running the Tree Trimmer or Baseball Bat pretty much a must-have. For the Baseball Bat, Charged Attacks essentially become kicks without the iframes and smaller stamina cost, Rush enables you to get more of these out.
Foreman - Gives you more mileage out of your kicks and also enables some funky loadout options if you're running the Expert version. Personally I think Kicks should deal Expert Foreman levels of damage by default, with the perk instead reworked to allow more zombies to be knocked down per kick or making them stay down longer when kicked by someone with Foreman.
Any item weight reduction perks - Pretty straight-forward, items weigh less, you can carry more stuff. In particular Healing Item Stack + Skilled Medic is a good combo, as it makes bandages far more weight efficient than first aid kits. Grenadier is pretty good too, more throwables + radios to carry.
Niche options that are pretty bad.
Winged - There is only one SMG in the game and you're not going to be using SMGs outside of their optimal range anyway due to the inherent gun spread in ADS. Pretty much a waste of a perk slot. They should change this so SMGs gain bonus headshot damage, or make Headblown also affect SMGs with Winged improving bullet pen for Handguns and SMGs?
Wicked - Just encourages you to waste ammo instead of going for the critical headshot to get rid of the zombie faster, better off just taking Headblown instead of this. I think they could rework it, so that all firearms deal increased stability damage, it'd make the weaker calibres have more of a presence late into a round.
Tight Shot - Shotguns in this game already have pretty tight spread all things considered. Not worth taking. Especially when you got perks such as Overkill and Scavenger which are going to give you way more bang for your buck if you are hyper-focused on shotguns. They should just merge this and Icarus together, in my opinion.
Locked On - Recoil on the MP5 is already pretty non-existent in semi-auto. There is next to no reason to use the other fire modes because otherwise you're just burning more ammo than needed. Waste of a perk slot. They could make Locked On, bring back the NMRIH1 Focus Mechanic, but for all firearms when stationary and ADSing for a long enough duration. Expert could reduce the time needed to 'focus', with both Normal and Expert giving the same damage amp.
Heavy Shoves - Damage on shoves is nice, but again kicks exist to put a group of zombies down and get 100% increased damage whilst they're knocked. You're better off taking Foreman instead. If they were to rework Heavy Shoves, they should make it stagger zombies instead of just interrupting them as well as potentially flinching zombies that the shoved zombie was pushed into, so it becomes a mini-kick.
Hard Blow - Very misleading perk as it only affects lights and heavies. Even with Expert, most 2-handed weapons just aren't going to see much use from this and the 2 handers which already do enough stability damage or have the ability to knock zombies down via charged attacks, aren't going to see much value from this. For example you need to be doing at least 20 stability damage to interrupt a zombie attacking you. The bladed 2handed weapons doing 20 on strong attacks only gain an increase of '6' if the compendium is correct, which means it still only interrupts and doesn't go into stagger (50) territory. There is maybe a niche use case if you run long wrench spamming lights for crowd control but that's about it, with the Baseball Bat and Sledgehammer you're going mostly be using charged attacks which Hard Blow doesn't affect at all. It'd be better if it affected both one handed and two handed melee weapons and overall stability damage of all attack types, or if it was reworked into affecting the cleave stamina drain on all 2handers, reducing the amount of stamina lost.
Resilience - Has very few use cases and when it could have a use, most of the time the hazards are entirely avoidable. Maybe it could be reworked to prolong the timer before infection completes it's cycle instead.
Reloading Perks - Guns generally reload pretty quickly in this game and the ones that don't have generous partial reloads, you also have shoves/kicks to give yourself enough time to reload. The only time these would be good is when there's multiple runners coming at you and you're stamina starved. If they were to rework the reloading perks, they should condense them in one perk a la Sleight of Hand. Right now currently with all gun reload perks split up into handgun/rifle+smg/shotgun I'd say it's entirely overzealous balance-wise and guns perks are already in a limited use-case situation as is depending on loot spawn RNG when it comes to the guns and ammo available.
Deprived - It's Thick Skin but it comes with downsides. Only really good for hard focused melee builds.
Adrenaline Rush - The benefits that this perk grants are not worth it because to maintain it, you have to be one slap away from going down, provided you aren't running Sturdy Body. This perk would be better off reworked into improving movement speed for a brief duration as well as heavily reducing all stamina drains for that duration when brought below 25% health before going on a minute cooldown instead of what it is right now or something along those lines, this way it would actually scale and synergise with other perks available such as Thick Skin and other health altering perks.
Eagle Eye - The M14 and Hunting Rifle already have pretty long damage fall-off ranges and due to how zombie spawns function in this game, you do not want to be plinking zombies from miles away when they'll just respawn closer to you instead. There's also far better options to take such as Penetrating Shot which are way more potentially ammo efficient if you can line a bunch of zombies up for headshots.