Here's my take on high-level play:
1. It's going to be more complex than lower level simply because there are more options. In combat, at low-levels you moved via your feet or your mount. At high-level, you do that and you fly, teleport, phase, and so on. It's going to be the same with spells, powers, feats, etc. If a player wants to make combat as fast as it is in low-levels by keeping the same level of complexity then there can be a couple of approaches:
a. Combat cannot grind. Maybe your fighter can dish out 25 hp in a single attack and gets two attacks for a total 50 hp a round on average. The typical big baddie like a dragon has 150 hp. You, as a high level fighter will be lucky if you have 80. Combat is going to be decided in about 3 rounds or less just from high-damage output vs. low hp thresholds. For some gamers this is really anticlimatic because it gets to the "He who wins initiative, wins the battle". High-level 3.0 did this (thank you haste, harm, and save vs. death). But this is an option. I actually loved combats in 3.0 because they were really darn quick.
b. The second option is to eliminate the options that make combat so complex. Get rid of the differing movement modes. Reduce the number of spells, feats, and powers altogether. An example is that a 1st level wizard casts one spell, a 20th level wizard casts a total of 20 spells over 9 spell levels. The risk here is that combat becomes boring at high levels.
In my opinion, I enjoy the complexity and the myriad of options. Combat takes longer, but my group and I find it rewarding.
2. The second thing about high-level play is how scaling tends to make rolling dice somewhat trivial because the numbers get so super high. For example, at 20th level, I have a +45 to hit against an AC of 30. The d20 roll is not really relevant except for auto hits and misses. If I'm a dual wielding scimitar fighter at 20th level, if my damage output is 1d6+25, the 1-6 range is kind of irrelevant as well. I remember when we got to epic level in 3.0 that we stopped rolling and instead declared average damage, did skill checks for taking 10 or taking 20 and so on. Some of the monsters I had for our epic battles had +112 to hit rolls (loved that monster).
So for #2, maybe I hope the math will scale down so that at high levels, the dice will remain relevant.
So my solution? Lower math, higher damage output, same complex options, lower hp thresholds. Combat gets decided in a few rounds. How to make combats last longer though? Have more baddies in the climatic battles. You just don't face off against a lich, you face off against a lich and his retinue of spectres.
I know for some players they wouldn't like this approach at all, and that's fine. I'm always open to other approaches for making combat go faster. There's really no right or wrong of it so long as it's fun.