Personally, I have a few issues with this.
They main objective of this rule is to nerf alpha strikes and give units a chance to act. I'm not too keen on this, as if model can really only move before they die, the phase felt pointless.
FYI, for mortal wounds, they auto fail the wound, and for poison weapons, they always roll on a 3 or less.
And to clarify, you do it on YOUR turn for YOUR models.
So first of all, I don't agree with the stated goal here, but I also don't think it accomplishes what you want it to. This removes the option of softening up a durable target before finishing it off with a melee unit. So no using the shooting phase to turn the odds of the upcoming fight phase in your favor.
This also basically makes any squishy melee units into suicide units. Sure, my banshees or wyches or whatever charged you and did enough damage to wipe out most of your unit. But now your guys get to stick around and wail on their low-toughness single-wound elf bodies before dying. Or maybe complete an action at the end of the turn even though they're all dead men walking.
Come to think of it, it's also weird that my banshees/wyches would then proceed to just... stand there during my opponent's following turn, possibly even getting to fight again if you charge me for some reason, before falling over like samurai in a Kurosawa film on my turn. It creates this odd delay/separation between the source of the harm and the actual harm itself. Like the bullets and knives take a couple of minutes to actually take effect.
So I don't think I like the stated goal as it kind of removes some existing tactical choices in favor of just letting units power forward until the end of the turn.
But also, this doesn't help against an "alpha strike" in the traditional sense because you'd be testing for casualties in your command phase. Unless "alpha strike" here just meant getting the drop on the enemy in melee. In which case, I agree there's probably a better system to be found than the current one.
In addition to the above, this proposal requires you track how many toughness saves each unit "owes" until the controlling player's next turn. You'd also either have to make this bookkeeping more complicated if there are any sorts of "special" wounds that make the toughness save more likely to pass/fail (such as the poison rule you pitched), or else ditch such mechanics and thus leave yourself with a smaller overall design space.
And as JNA points out, removing toughness from the equation isn't great. Being able to model a meltagun being better at hurting a marine than a lasgun is probably a good thing.
So overall, it seems like your pitch
* Creates extra bookkeeping.
* Reduces tactical options.
* Creates a fluff/crunch disconnect (delayed deaths, removes ways to model "strength", etc.)
With the only real "benefit" being that units have a chance of punching the enemy before they die *if* the enemy opts to get into melee with them. Which I see as more of a negative than a positive as it screws over fragile units.
Not a fan of this one. Sorry, friend. :(