[Miller]

Regarding this though, does not dropping the GUI tax to do damage achieve kind of the same result? 

I feel as though LUC could use 1.5 Crit per point instead of 1, as giving STR crit will just see LUC drop in usage a lot of the time. 

GUI is not an objective requirement to play the archetype, it's not a 'tax'. The amount of damage people are okay with is subjective and varies between everyone but the ideal number for a critical build to function with some level of consistency is 75~100 + the amount of CEvade granted by APT. (14-16 not including racial bases) doesn't really ever change. GUI scales worse than STR barring times where there's a heavy amount of flat bonuses, so it's also typically the stat you dump into last once you have the rest of your essentials sorted out. (RoT+, Claret, Checkmate, Ether Invitation, Elengrave for said flat bonuses)

Raising LUC would lead to everyone being able to build less LUC to reach their ideal crit rate threshold, I'd prefer if LUC got more defensive value if it was buffed honestly.

I can see the concern with people foregoing LUC for STR if it did have crit chance yeah; in the instance where STR has crit attached? It'd need to be a pretty low value and also be tied to the base stat akin to HP. 0.25 Crit per point of strength would give these builds at least 10 points of stat freedom at the very least.

As for critical mechanics being underwhelming? Absolutely.
A few like poise could use a tune up for sure, though I prefer if everyone could hit a baseline with just stats and equipment choice.