Our group is low level but our experience has been that "deadly" encounters really are deadly. We've had numerous deaths and near TPKs. But I think the landscape might change at mid and high levels. What I've observed as a player is that more monsters make the battle a heck of a lot harder than I would probably have anticipated. Also, going into another battle just after completing one big battle is tough.
It's a consequence (perhaps unintended) of Bounded Accuracy that the impact of being outnumbered is out of proportion with the impact of being outclasses. That is, one monster worth 10,000 exp is not as great a threat to the party as 10 monsters each worth 1000 exp. That's often counter-intuitive. You think (as the guy who wrote HotDQ must've, "wow 1/8th CR, better have at least 8 of them to remotely challenge the party." Nope, those 8 kobolds can quite easily TPK a first level party who'd roll over a lone CR 2 monster worth more exp - conversely, the party just might erase all 8 of 'em in a surprise round, if they happen to have the right spells prepared and just cut loose.
Long fights aren't necessarily fun
Not necessarily, but they can be interesting, and they can get the whole party involved, and allow for tactics to develop and play out. A campaign that consisted of only long, challenging battles would be monotonous, as would one that fell into a rut of short, trivial combats - or, worse, short, deadly ones. A system (and DM) needs to be able to handle a wide range of possible challenges. Short/trivial challenges are actually pretty easy to deal with, they don't take much time or prep and can even be hand-waved without losing much.
The real danger of a long fight being boring comes when the DM has to softball an encounter to avoid a TPK - you see this with inexperienced DMs all the time, they set out the encounter, the party starts getting beaten harder than he expected, so they start fudging the monster side of it - misses, low damage rolls, bad tactics, whatever - and if the PC side doesn't do much better, it can drag on and on in an increasingly desperate and improbable wiff-fest. Very sad.
and in 5e, they generally reduced monster hp from previous editions and increased damage
At low levels, they decreased monster and PC hps. At higher levels, they're as or more bloated than ever. Hit points - both HD and damage output - is responsible for more of the scaling this time around than attack/AC/saves (that Bounded Accuracy conceit, again). Not only is accuracy bounded, but it's higher for most characters, closer to 60-70% or so, instead of around 50 or a little better. So there's lots of hitting, and the primacy of 'focus fire,' surprise, and offense-over-defense strategies is encouraged.
Now, it's a matter of taste if you find fun or not, but even if you don't, at least you don't have to put up with it for long.
And, that's really the bottom line when it comes to the 'fast combat' ideal: it assumes that combat just is not the best, nor even a particularly tolerable, part of the game. Some combats will be fun, but not last; others will be awful, but mercifully brief. Either way, the fun of the campaign has to come from somewhere else.
Conversely, while more involved combats can achieve some tactical depth or drama to provide interest, that's also a matter of taste - and if you don't like it, well, they're /not/ over quickly. But, with Bounded Accuracy and the way 5e is tuned, that's not really an option. Any battle with enough opposition to take a while to resolve is going to be too deadly to run very often - and, thus also runs the risk of turning into a fiasco if the DM feels the need to softball it part way through.
Obviously, the more a game is tuned for 'fast combat,' the more profound the advantages accruing to system mastery may be, pushing it towards 'rocket tag,' if the DM responds by ratcheting up the offense on the other side, as well.
