It does have an impact, but not that much more than having a cybernetic limb.
And definitely not so mich, that it would take a slot where another thing doesnt.
The loss of a limb alone, along with the phantom pain and neural damage can be reason enough to lose a slot.
Okay, it's obvious it's your idea vs ours, and since we lack the actual hard knowledge of how this tech is supposed to work, it makes no sense trying to convince each other which explanation we just pulled out of our behinds makes more sense.
So let's just get down to things that we can actually gauge, like the effects it has on gameplay and setting. And here, your idea is plain horrible.
From the gameplay perspective, bionic replacements are, well, replacements. They may have some additional utility to them, but at their core, they make the difference between being able to keep playing a character and not being able to do so. This is quite important in a system where each hit is resolved on a big bad table of horrible things that's about half composed of you losing vital body parts. It's a ridiculous idea to prevent people from getting those replacements by any means, and it makes a mockery of the fate threshold - yes, I totally survived that shot, and could keep playing that character, but unfortunately the crit effect of missing my heart stays and I don't have enough Toughness to install a replacement, so I guess I'm dead anyway, or permanently bedridden. Yes, that's a great, fun way to handle things! On the other hand, augmetics are simply extra utility that you can put on your character. They're never vital to playing the character, just something cool you may want to have. Due to that, and because stacking too much gear that's always within reach and which cannot be taken away can be bad for gameplay, it makes sense to limit the number.
From the setting perspective, bionic replacements are either a religious observance or a simple matter of convenience. Unless you're an AdMech nut who obsessively replaces every bit of flesh with blessed metal, most Imperial subjects get bionics when they lose important body parts in the course of duty. The practice is exceedingly common and treated casually, and you have to stoop to the lowest rungs of outcast scum to find truly crippled people. On the other hand, augments are handed out much more sparingly, only to people who need them to perform their job, be it auger arrays for explorers and scientists or those creepy hands for scribes or whatever stuff Tech-Priests keep sewing onto their bodies in the pursuit of their god. AdMech is pretty much the only place where you'll find people installing extra augmetics simply because they can. From that perspective, it also doesn't make sense to restrict replacements in every way, and I've never read anything like that happening or even being alluded to in any source material. Guardsman loses hand fighting an ork, guardsman gets a new metal hand, end of story.