Possible basekit idea

As wild an idea as this is, I agree.

I fidgeted with an idea awhile back called the Groggy status effect.

The idea would got that Survivors would start the match with Groggy 2 - Repair speed is reduced by 24%

When a survivor enters chase with the Killer, survivors lose a stack and have Groggy 1 - Repair speed is reduced by 12%

When a survivor takes damage by any means, all survivors lose the Groggy status effect completely.

What does this do?

It will be slightly annoying for survivors, yes, and culls quite a bit of their initial momentum. But let's consider it.

Top tier killers such as Nurse, Blight, Kaneki, and even Hillbilly to an extent will enter chase rather quickly - and oftentimes get hits within a few seconds of a match starting, making this "basekit" moot and staggering survivors by only a handful of seconds worth of progress.

Bottom tier killers that require time for setup such as Trapper, Shape, and even Hag would see massive benefit, with survivors suffering from Groggy for several seconds before the Killer enters chase and starts damaging players.

In this way, lower tier killers would see a massive bump and be able to make matches much more tense, close, and play more confidently while high momentum killers will find no true benefit from it.

As a tertiary benefit, survivors will learn to grumble less when a health state is lost.
When the Yui gets into chase in the first 5 seconds and takes a hit shortly after - the team's thought isn't going to be "Well, might as well pack it in folks, this match is over, where's the DC button" and would be elated to see their progress bar lose the red hue while saying "Finally, lets use the toolbox now."

While 24/12% sound like a lot in theory, the duration of the debuff and severity of the repair hinderance would do relativley little overall to destroy a team's ability to escape and would promote much more healthy behaviors in the long run.

4 survivors spread out on generators and it takes a Blight 12 seconds to get into chase, 20 to land the first hit: Instead of gaining 72 total generator charges - they'd gain 60, and the debuff would be gone for the rest of the match.
Vanilla - 3 generators at 22%, 1 at 13%.
Groggy - 3 generators at 16%, 1 at 10%

Same situation but it's a Trapper that takes 40 seconds to get into chase, 60 to trick a survivor into stepping into a trap: instead of gaining 220 charges of generator repair, they gain 175
Vanilla - 3 generators at 68%, 1 at 45%
Groggy - 3 generators at 52%, 1 at 33%

So in a top tier killer match it might bump the initial survivor momentum down by 3-6% of repair, but for very low momentum killers that are at the bottom of the tier lists, it will bump initial survivor momentum down by 12-16%

It's not usually going to be game changing. Those spare 5-10 seconds aren't going to be what makes or breaks a survivor's game, but it will organically promote healthy gameplay behavior, give lower tier killers more breathing room, and won't do much for aggressive higher tier killers in the short or long run.

I also liked that it can fit in the lore, as survivors fall asleep at the fire and awake in the trial - so them being Groggy and needing something exciting to shock them awake is nice.

No Mither removing the effect for the whole team is a hidden bonus.

~~~~
Edit:
Percentages can easily be changed to be more mild. 24/12% is the maximum I'd suggest - which would have the most radical and definitive effect on gameplay, but can be changed.
A silly rule of thumb is to consider that every 4% that a Groggy stack contributes puts 5 seconds of game time in the pocket of Trapper and Shape, and puts 1.5 seconds of time in the pocket of a Blight, Nurse, or Kaneki.
12% giving Blight players ~5s and Trapper players 15 seconds is a bit strong, but I personally think it's worth investigating.
Lowering it from 12 to 10, 8, 5, or even 4 are also viable options. While I favor 12% as the maximum yield, it would be a gameplay element that can be tweaked to augment early trial behavior.