Lets go through the actual steps:

• Roll a death save
• choose an action
• calculate new exhaustion level (which is completely different to the exhaustion mechanic that's already in the system)
• roll relevent attacks etc at new penalty

So not super complicated, but definitely much more complex that.... basically any other way of dying. When added to all your other homebrew rules it doesn't matter if nobody cares until they reach 0hp, because the flip side is that they have to learn another new rule once they reach 0hp.

Meanwhile though, dying has moved from a serious problem to a non-condition: there are some mild penalties for acting, but overall? You still have all your actions, just at a slightly slower, still costless, move speed. Players lose little for entering it, so are going to be much less inclined to avoid it, while monsters are now encouraged to double tap - it would be very stupid to walk away from a PC just because they've been knocked prone, even if their actions has an additional cost now.

You're adding elaborate "adaptations" to your reliant robin to stop it tipping over instead of just cutting your losses and buying a car with 4 wheels. Spending lots of your time on something doesn't make it better than what's already out there.