Combat encounters while traveling in 5e

I'll cut right to the chase: as much as I love 5e (I've been playing since 2nd edition,) it's not perfect. One of my main beefs is the fact that combat encounters during travel, unless they're very, very dangerous, are pretty trivial.

Since the PCs get everything back after a Long Rest, Hit Points most importantly, it really minimizes the danger of having a combat encounter on the road, unless it's very dangerous or there's going to be multiple encounters in one day. Back in 2nd, when healing took a long time (at least until your Cleric got to be higher level,) you could wear the party down by having encounters over a series of days. Now that doesn't really work.

I'm not complaining, I just want to see what everyone else does.