Well, since crappy combat is the main reason I haven't touched Skyrim in ages I'd say a complete overhaul is in order, but in the interest of time and since backstabs seem to be the popular topic, I'll just talk about those. This is going to be a bit long.
In response to OP's idea there are some problems with it. Primarily you've put in a mechanic that lets you insta-kill enemies even if you don't have the stat skills to do so. This seems wrong to me, especially seeing how dead set on skills you are. If you haven't raised your backstab skill high enough to assassinate a target, then you shouldn't be able to assassinate them, QTE or no. I am sympathetic to the uselessness of basic weapons, but you've overcorrected in making them a one shot kill, or a one shot kill after a QTE if you don't have the skill high enough.
The way I'd change backstabs would have to do more with positioning and stealth (which would be significantly nerfed as most people here have suggested). Backstabs would work in tandem with stealth, sneaking up behind your target without them noticing you is, obviously, the first thing you'd have to do. Once you're behind them and take your first stab the stat skill system comes into play. There would be several levels of backstab skill, at least 3, possibly more, which would apply different base-damage and crit-chance modifiers to your weapon's basic damage number. For the lowest level skill, a backstab would receive a fairly small base-damage mod with a varying crit-chance mod based on how you are positioned behind the target; in a 180 degree zone marked as "behind" the target the highest crit-chance mod would be at 90 degrees (directly behind the target) with lowering crit-chance mods as you get farther away from direct center, to nearly zero crit chance at 0 and 180. This helps the backstab mechanic work along with stealth and player skill, as you do less damage and are more likely to get caught trying to backstab as you get farther away from 90 degrees. When you actually make the attack there are two outcomes: 1) You backstab correctly (at low levels), represented by a crit ([weapon damage + backstab base-damage mod] x crit mod), meaning you've stabbed your blade all the way in and have done significant internal damage. The crit mod making appropriately leveled backstabs typically one-shot the target. 2) You flub the backstab (at low levels), represented by a non-crit, meaning your inexperience with backstabbing caused you to "stab" armor, or bone, etc. and only cause minor damage (weapon damage + backstab base-damage mod). At low skill levels these non-crits are unlikely to out right kill a target, but do significant damage (close to what melee focused weapons i.e. sword, axe, etc. would do), and possibly stun the target long enough for you to try hiding again to set up for another attempt.
As you put more points into the backstab skill your base-damage mod would increase, your crit-chance mod would decrease in damage (possibly decrease/increase in likelihood), but have a more uniform % chance at wider angles. This would stabilize the damage curve of your backstabs as you put points into the skill and get better stealth abilities, having it rely on partially random crit-chance mods for damage at low levels, and produce high damage even without chance-based crits at high levels. Having backstab base damage go up and crits go down at higher levels is a good way to represent the natural progression of skill as the player character learns how to properly backstab, makes fewer mistakes, and become more proficient and reliable. Over leveled backstabs are likely to kill targets even without critting.
Something else would be to improve the AI of surrounding enemies to the sounds and results of an attempted backstab. Like if you backstab someone while they're talking the other enemies would react to it, or a failed backstab has the target calling for help / alerting other enemies.
The last bit I'd think to put in off the top of my head would be a system to vary how different armors react to backstabs. Heavier armors would resist, if not be outright immune to, backstabs; this could be represented in a number of ways like reduced modifiers or negative modifiers etc. Another idea I find interesting for higher level backstab play is having high level armors with different crit-chance and resistance zones, for instance an armor set that is immune from backstabs directly behind it, but vulnerable at the sides. A skill letting you see the vulnerabilities of different armors would be more or less required for this last part to keep it from becoming a trial and error process though. This would keep the game of sneaking up on an enemy interesting even at higher levels, compensating for the player's higher sneak skill by requiring them to expose themselves to perform a backstab.
All that ^
Is basically how I would rework the backstab system in Skyrim / TES without changing too much of the game, though as is it's a little rough and I'd still need to mess with it. Most of the systems would be fairly easy to implement and the player would never be slapped in the face with them outside of the "armor vulnerability skill" thing.
TL;DR
Backstabs are based on how well you can sneak, positioning, weapon power, and luck-at-low-levels. Even crappy weapons at the lowest skill level can kill appropriately leveled enemies. You can significantly damage, but not out right kill, enemies outside your skill range with backstabs. Failed backstabs encourage you to run, hide, and then try again once the enemy lets their guard down.
Holy shit this went longer than I though it would O>O