The session I ran last night was specifically crafted to push the bounds of what the party could do, being essentially a series of "difficult" to "deadly" encounters (with no single creature with a CR higher than the party level, but lots of creatures generally), and I learned some very interesting things from it.
First of all, was that the fights got grindy, grindy, grindy. After about five or six turns? Everyone's like "Sheesh, can't either the monsters or us just DIE already?" 5E characters, once they're out of the 1-2 level range, are surprisingly hard to kill, so if you put them up against something equally hard to kill, you end up with both sides just pounding away to no effect.
Second, the 15 minute workday was back. Each encounter was followed by a short rest, and the third encounter made them stop for a long rest. They were out of spells, out of class abilities, out of hit dice, and frankly just fed up, and wouldn't press forward for anything.
In short, it felt like being in the sloggy parts of 3.x/PF again. I wasn't terribly surprised, having read The Alexandrian's history of the 15 minute workday problem, but it was still interesting to see it in action.
So yeah, I won't be doing that again, or at least, not as an extended series of encounters. A big fight like that as an occasional set piece I can see being cool, but for the "bread and butter" encounters, the difficulty needs to skew closer to the 5E standard or you end up fighting all night and feeling like you aren't getting anywhere.
-The Gneech
