But if we allow monsters to negate crits by sacrificing shields and taking fatigue, we might as well just remove crits altogether.
well i think it is relevant to remember you can only take fatigue to negate a crit once per short/long rest. so really at most any given monster will negate 2 crits, most of the time only 1
if they want the fatigue. so...there's that.
Rules for negating crits were likely put in place to reduce the unpleasant swinginess of 5e combat to the players detriment (something that 5.5e is also doing by basically removing monster crits, at least if things didn't change since last time I checked).
the second 5.5 playtest reverted back to the PHB rules, but either way...what? i mean, ok, sure, at lower levels lucky crits can screw the players, but beyond like level 3 it's not really a problem. i find this to be a bit of an odd assumption to make. i mean, maybe you're right, i dunno, but i'd've never even considered it had you not brought it up.
If we cannot assume that this asymmetry for negating crits is for the benefits of PCs only, we also have to conclude that the a5e berserker is essentially flawed, since it's defining feature (which cannot be triggered by the player and it occurs spontaneously quite rarely, btw) can be negated by every monster.
well again, given where and how sacrifice shield and fatigue are written, i don't think we can assume that, so i think we have to conclude the berserker is flawed.
I'd rather err on the other side and assume that crit negation is something only PCs and very specific monsters can do.
and that's fine - my point, again, is that as written, i think many narrators won't make that assumption. i mean, OP sure didn't, and honestly if i ever ran an a5e game i probably wouldn't either (though, again, i'd definitely make it so fatigue effects monsters immediately when gained in combat instead of after, solely so that it actually matters in play).