One would think that a Sheriff could do such things but he never wanted the Sheriff to leave his side.
Well, there is a moment when he says 'You've been trying to wipe them out for weeks. He did it [wipe out the LA sabbat] in a night!'. So that's not the problem. The Sheriff just never had the opportunity you had. Or he was simply canonically too weak to do a frontal assault on Hallowbrook.
I don't think LaCroix was inexperienced per se. He is young relative to Camarilla Elders, but that doesn't mean much. He's probably one of the oldest vampires in LA and that did not avail him. Abbrams, Therese, Nines are all younger than him and competent at what they are trying to do. Which is way less than LaCroix. Strauss comes across as more experienced than LaCroix, but the thing is that Strauss never tried to be Prince of LA. He's ok with being Tremere Primogen.
The problem I think is that LaCroix is just in over his head. He comes across as this up and coming new talent from the west. Napoleonic Wars generation. A mere child in old world terms, still doesn't amount to much among the elites of core of Camarilla USA but he's got some connections and powerful pawns. So he tries his hand at the frontier. Los Angeles is the boonies of the atlantic vampire world and to LaCroix the sudden chaos from the Kuei-Jin invasion must have seemed like an opportunity. He'd enter the city and restore the balance of power between Kindred and Ghost, he'd be the savior of both Camarilla and Anarch. But then he continuously failed to bring people to heel. The Anarchs, predictably, resisted his rule. That would have been much less of a problem if the Sabbat hadn't invaded LA as well, if the Kuei-Jin didn't prove to be so disciplined and powerful, and if the LA Camarilla Primogen themselves didn't resist LaCroix's rule as well. Strauss is loyal, Gary and Grout not so much. LaCroix was a middle manager who was probably good enough material to stake domain elsewhere in the pacific coast, but LA turned out to be a job for an Elder.
A coward wouldn't do these types of power plays.
I suppose. Still I think you'd agree that LaCroix is no warrior-prince. His power play consists in acquiring powerful pawns, and never in himself as the tip of any spears. He'd sooner dominate suicide bombers than show his face in battle. So while I do stand by the word coward, I'd add the word toady as the most important qualifier. He must have spent the last centuries being a sycophant in someone else's court. He defers to power by default and even once political power is his own for the taking he continues to act obsequiously towards his minions. Be them the Sheriff or his Wunderkid. They are his Fighting Men and they exist to be blackmailed or flattered into service, not necessarily subjugated by his own hand. He must be the sort of person who is confident in his own magical powers and likely to use Dominate as a crutch. After all, there is no way anybody in this far away forgotten city in the californian desert is of a lower generation than him, right?