Is it
possible to build 5e PCs who don't meet this floor?
Maybe, I guess, but you'd have to work pretty hard at it, wouldn't you? Would a party of Rufus's be below this floor.
@
Hemlock, you are following along and have excellent 5e build/resolution intuitions. What do you think?
It depends on the Easy encounters. Obviously it's possible to build Easy encounters which will wipe the floor with any level of PC party--e.g. a bunch of glass cannon CR 1/8 creatures, all of them with Flyby, Incorporeal Movement, and 100' of flying movement. Even if you increase the challenge level by one level per DMG guidelines to represent terrain favoring the enemy, that just bumps them from "not even Easy" up to "Easy." The lesson there is that "the DM can always cheat (but shouldn't)," or in other words "don't fool yourself into thinking you're building a fun game just because you're following DMG guidelines."
However, you were asking a question about PCs, so let's say we're discussing Easy encounters constructed randomly and not tailored to the players, e.g. Easy encounters from kobold.com or a module (Curse of Strahd) that are Easy because you're playing a module with higher-level PCs than expected. Furthermore, by "at least 51% of the time" I'm going to assume that you don't mean "can't get past a single Easy encounter 51% of the time," but rather "can't get past a full days' worth of Easy encounters at least 51% of the time," because obviously even a party of Rufuses played by ignoramuses could beat a
single Easy encounter.
Furthermore, I think we have to set aside Combat As War techniques, thinking outside the box, winning through roleplay/negotiation/making alliances/etc., and talk purely about combat challenges. Your question then is, is it possible for me (as an adversarial PC-creator) to create a party of four PCs so bad that I (as a player) couldn't use them to win a DMG-specified adventuring day full of straight-up Easy combat at least 51% of the time?
I believe the answer is "Yes, I could." It takes some fairly extreme measures, along the lines of creating a PC without any Extra Attacks or attack cantrips and whose best combat spell is Witch Bolt. I don't think a party full of Str 6 Barbarians would qualify, but a party full of Str 3 Dex 3 Gnomish Barbarians might.
Edit: huh. On reflection, and after doing some quick kobold.com checks of the Easy encounter threshold, those Gnomish Barbarians might very well be unable to beat a single Easy encounter 51% of the time after all. They're really quite bad.