Although I see potential in the tweaks made in the Combat Update, I feel like they're still rough and need more fleshing out. I'm not entirely certain how Mojang wants to go about this, but I can think of a few ways to tweak the existing combat system to make it more usable.
1. Lower the cooldown slightly for swords. Now, I'm not asking for it to be lowered too much, to the point where sword spam is a viable tactic again, just to the point where you can attack at a similar rate to pre-1.9 combat. The cooldown period would mean that you can't sword spam as before, but you can still rush in with a diamond sword and kill most overworld hostile mobs in 3 slashes or less. Speaking of slashes,
2. Buff the sweep attack and make it toggle-able. One of the biggest problems with 1.9 combat is dealing with groups of mobs up close. To mitigate this issue, Mojang added a sweep attack that would deal a small amount of damage to surrounding mobs and knock them back. Despite this, it's still easy to be overwhelmed by several mobs, especially if they're not clumped together in a group. A solution to this would be to buff the sweep attack, maybe by making it deal more damage. There are probably better ways to buff it, though, but I'm not entirely certain of what they would be and how they would make sense in the game. The next part of the suggestion is a way to toggle whether or not you want to use the sweep attack. Many people have complained about accidentally hitting their pets with the sweep attack while fighting mobs. A good way to tweak this might be to make it so that you have to be sneaking in order to use the sweep attack. Better yet, maybe a toggle should be added to prevent the sweep attack from hitting pets.
3. Tweak invulnerability frames to be the attack speed of the weapon divided by 2 or 3. I'll admit that this system was
stolen from inspired by a popular 2D combat/exploration-based game with a pixel aesthetic involving blocks, but Minecraft has stolen ideas from been inspired by many other games before, so this wouldn't be too much of a stretch. It would also allow for tools/weapons with a lower cool-down, like pickaxes and hoes, to become more viable for combat.
That wraps up my suggestion for some minor combat tweaks that I feel wouldn't drastically change the game's spirit but still improve the game overall. Feel free to leave feedback, including constructive criticisms, if you'd like, and please let me know if I screwed anything up on here, as I think this is my first suggestion post to this forum.