DMZ2112
Chaotic Looseleaf
My feeling is that variety will come down to the ability of the DM. I love that. If you want to do something creative, the DM must come up with a ruling on the fly. He has a simple mechanic to work with to do it. All the old things are possible, but the DM and player have to discuss it an work it out.
But then it's not up to the dungeon master, is it? It's up to the players. I can't give a ruling on something I'm not asked.
Scouting and movement are fluid now. I haven't had so much fun scouting ahead and taking out sentries in ages. Passive Perception against Rogue Stealth is good fun.
...That's because stealth always wins!

Now with 5E, you can move, attack, move, attack, bonus action disengage, move to cover. It's so much more fluid, imaginative, and fun in my opinion. Until people get older mechanics out of their head and understand the new fluidity of combat, it will seem less varied when it is actually more varied.
I agree that the rogue class almost forces a player to "think D&D5," if you will, but that's cold comfort to a fighter. I do like that our party has four fighters and they are all unique, but in terms of actions all they do is pound on bad guys. They just use different implements of varying bluntness.
As I said, they don't seem to mind, but I do. One thing I definitely plan to do after the campaign leaves Phandelver and transitions to Solamnia in a few weeks is design encounter spaces with more opportunity for tactics. We don't use a battlemat, but even so the encounters in Lost Mine have been very straightforward line-of-skirmish style conflicts.