If I'm engaged in a relaxed game, why must I resort to using tricks to "speed up my combat"? I'm talking about the type of tricks mentioned in several threads about speeding up 4E's combat - halving monster hit points, having PCs roll attack and damage together in the same roll and all the other "tricks" people have presented just to get their combat down to a reasonable time span. Why can't the game just present a combat system in which you can resolve the situation in a reasonable amount of time in the first place. Why do you have to kludge the system to make it work for you? Why is it acceptable?
I haven't found I've needed to cut HPs in half - I gave a similar idea a shot, a while back, but didn't find it added anything to my game. I don't find that I need to kludge it at all, actually. I use a program called Masterplan to make my DMing even smoother, but I can go without if need be.
I think one of the issues you're running into is that 4e's combat is intentionally highly-interactive and highly-tactical. It's not a combat engine you can just let run on autopilot, and it absolutely runs best when the players and DM are both engaged with it.
I'd say if your main goal for combat is kicking back and not worrying about tactics and preparation, and getting fights over in 15 minutes, 4e (and 3e) past the first few levels probably isn't what you're looking for. I'd look towards one of the OSR games, or maybe at something altogether different like WFRP2.
I think any RPG that requires you to rush through combat by using various tricks or techniques is a telling failure in that part of the game. A combat can be dramatic and exciting without having to be rushed. I don't want to be hastened through running a combat just so I can get it to be over with in a half-hour to hour instead of two-hour, three-hour or longer combats in an RPG. If I can't play through a combat at about the same pace I run the rest of the game and reliably have 15 minute to half-hour combats (or about the same length it takes a group of characters to interact with an NPC or search a non-empty room in the game), I think that's bad game design - a faulty focus placed on one aspect of the game over another portion of the game.
That's just it, though - it's not a failure in game design. It's a failure of the game to match your expectations. Hour-long combats are built into the system, and longer combats are expected for major battles. And more than a few people are having great fun with 4e as-is. Quite a few more find it works great for them with some "kludges" which you'd rather not deal with. And quite a few yet more find that it doesn't work for them at all.
4e was never designed towards 15 minute combats. Yes, those can be fun, too, but that was never a goal. Other games
are geared towards quick & easy combat; not every game
has to be.
I'd probably say you're playing the wrong game if you're not enjoying it, if it's not meeting what you want out of your RPGs, and if you would rather not put effort towards making it work better for you. I'd try some other games that will work better for your expectations out of the box.
-O