we've decided to have a philosophical discussion here.
This is not philosophical at all It's purely technical.
You raised timeouts of 3 and 10 seconds to 5 minutes and declared essentially that we can't make these timeouts high enough. I'm saying we sure as heck can!
I totally get that
If you totally got that, you wouldn't just assume 5 minutes is a good number and say that the timouts should just be super high.
The chances that 2 minutes or 1 minutes or 30 seconds is better seems pretty likely. Why not make it an hour with your philosophy?
If you are debugging, there is a big difference between 1 minutes and 2 minutes and 5 minutes.
So you see, I'm focusing on the very specific and technical timeout raise that you made. Your philosophy of "the timeouts can't be high enough" also concerns me, but what has my focus is that this issue indicates tests usually pass with timeouts of 3 and 10 seconds and you are raising them to 5 minutes and that seems overkill and comes with negative consequences that are pretty likely not necessary.
It's pretty easy to spot these kinds of failures. It's way better to do a more sensible timeout, and if there is another fail, double it again or something.