So, my question is three parts:
1) Do you feel D&D combat is slow (or "drags")?
No, not for us. Large numbers, summoned creatures, polymorph effects, and some other spells can really draw combat out, however.
3) Has it always been that way? I'm not familiar with very much of 1E or 2E.
Compared to 4e, 5e is
light years faster. 4e combat had a
lot of potential moving pieces. Hp were moderately too high, and when you got to higher level there were a lot things going on constantly. Large combats at high level took hours and could be mentally draining, IMX.
Compared to 3e, 5e is moderately faster. 3e was incredibly fiddley in terms of bonuses, and it took much longer to resolve a lot of combats than 5e. Sure, certain spells could end a combat immediately, but that was pretty rare, IMX.
Compared to 1e/2e, 5e is somewhat longer. The thing about 1e/2e is that you might run into a situation where stuff didn't make sense or you'd have to look stuff up, or you might have several save or die effects and it'd be over right away. 1e/2e also tended to involve a lot more missing, especially at lower levels. HP were lower, but damage rolls were even lower than that. 1d8+2 was
a lot of damage in 1e/2e. Also, the core attack roll in 1e/2e is slightly more complex which makes things just a touch slower. Even if the combat rules are bare bones, players and DM are rolling perhaps a dozen attack rolls a round. That time adds up. Like, there's a reason combat wheels for 1e/2e exist and not for 5e. Also, if you're playing with the full initiative system (melee/missile/spell, weapon speed, casting time, managing round segments, etc.) the game could be a
lot more complicated. IMX, nobody actually did that, though.
Overall, I think 5e is about as simple and straightforward a systems as we've had. Other editions could have combats run faster than 5e, and you can certainly run 5e in a way that combat goes slowly, but in general I think it's fairly fast for a D&D game.
Bear in mind that the way HP increase with level means that D&D is kind of inherently an attrition-based game. Characters are expected to survive multiple hits. Lots of RPGs have NPCs die in 1 hit unless they're specials.