First, let me say that this is an interesting idea, very thought-provoking. I recommend actually using it, too – practice always, always trumps theory, and a play-test will tell you so much more than sitting back in one's armchair and going “I feel that....” After all, the bottom line for house rules is that if it works for you, then it's a valid part of your arsenal.
That said, on the theoretical level I'm inclined to raise objections.
1. I like combat that allows for both sides to miss. Done right, it can build tension nicely. Perhaps the major factor that makes a difference here is how long a “round” is for you – verisimilitude allows more hitless six-second rounds than minute-long rounds.
2. I <i>really</i> like combat that allows for both parties to hit. It's something that happens all the time in real combat, for one thing. In game terms it increases your dramatic options and adds a little tension and variability that are lost in a winner-take-all setup.
In fact, this is one of the biggest downsides of the system you propose: in winner-take-all, whoever has the higher CR is even safer than they would be under standard rules, and almost guaranteed to win a fight. (This only gets worse if you use the “seizing momentum” rule!) Elements of chance, and hit point totals, also come into play of course... but all other things being equal you're creating a system that statistically encourages PCs to bully the weak (boring) and refuse to ever engage the strong (also boring). Gone is the ability of a party of first-level characters to gang up on a Minotaur and overwhelm it with numbers.
It's also worth pointing out that you threw in several tactical options that allow both sides to hit and damage, or both sides to do nothing. To me this says that you felt the lack of each potential outcome and tried to find a way to put them back in... but in the end, I suspect that this is a net increase in complexity. It doesn't seem worth it to me to make the players memorize a bunch of little situational rules just to speed up combat by one roll per round.
3. You comment about a fighter being able to hold off a monster that s/he can't hurt. There are plenty of other rules that give this ability in a more beneficial way, though: a full-defense action or the Combat Expertise feat in 3.x-style combat, for example. It's easy to see why a defensive option that increases your defense in some way is better than a “defensive” option that consists of counting on a string of useless wins.
4. I <i> agree</i> that dynamic, skill-based offense against static, equipment-based defense is problematic. However, there are other ways to deal with this that doesn't involve collapsing all combat into a single roll. For example, making defense into a skill check. You could even go the GURPS route and give players the choice of defending with a Dodge, Parry, or Block roll, with various upsides and downsides to each choice.
5. The averaging-out of damage from multiple monster attacks seems pointless: it loses the “flavor” of bites being different from tail slaps (for example), and you always had the option of a monster simply choosing before rolls are made who to target with what attack.
So that's my two cents. I recommend play-testing this style of combat to see how it feels. But it strikes me as a less-than-ideal solution to certain problems, and an unnecessary “solution” to several situations that aren't problems at all. Keep up the brainstorming, and good luck!