I'm getting the growing sense that the Louisiana Lion is held in far higher esteem than he deserves. Even in my Jenny Barnes deck, he never quite managed to carry his own tremendous weight. In my "Skids" O'Toole and Finn Edwards decks, he might as well have been a blank card for all the good he did.
First of all, a fourth action will not make an investigator 33% more effective - not even close. Investigators run on cards and resources, and any kind of "once per round" economy the investigator has (including the usual card and resource during upkeep) will be spread much more thinly over four actions rather than three - fewer resources to pump into Hard Knocks, fewer skill cards to commit to tests, and fewer charges of Flashlight, compared to the number of actions you have in which to use them. You could always use the extra action to draw a card or gain a resource, but if all you want is some drip economy, why not just run Lone Wolf or Pickpocketing, which pay for themselves much more readily?
Second, unlike most of the other pricey allies, Leo doesn't give any skill bonuses - you'll be taking more actions, but you'll waste a lot more actions on failed skill tests. For example, Dr. Milan Christopher's +1 makes the actions you have that much more efficient, and he's cheaper to put into play and serves as an (admittedly slow-to-wind-up) economic engine. See also Peter Sylvestre, Cat Burglar, and of course Beat Cop.
Third, by occupying the ally slot, he prevents you from playing those other aforementioned allies.
Fourth, he's crazy-expensive, which makes him awkward to play in most situations:
Getting him out early costs one more than your entire starting resource pool. Unless you're lucky enough to draw him alongside Hot Streak, this is a crippling opportunity-cost; he's going to be your only significant asset for the first few rounds.
Getting him out midgame has a similar (but more manageable) opportunity cost, but he takes so many rounds to pay for himself that he may just barely break even by the end of the scenario, and in the meantime you've deprived yourself of the tools that might have rescued you from a dire situation if you had run a different card and not sunk a small fortune.
- Getting him out in the late-game is usually a waste. If you only have a few rounds left, you should be able to spend six resources on something more worthwhile than two or three more actions spread over the remainder of the scenario.
And all of that assumes that you aren't forced to discard Leo early because of an Encounter card, which could be a serious possibility depending on the scenario, especially if he's your only asset in play at the time.
If anything, his relative economy actually gets worse for high-XP investigators. In the Rogue class, Streetwise is a fantastic way to pump skill tests, and it plays better with high-efficiency limited-use cards like Lupara, Deduction, and of course Double or Nothing, not to mention the highly efficient pumped "Watch this!". I'd much rather move once and take two amazing actions than move once and take three mediocre ones.
Therefore, Leo is at his best when paired with cards that can turn actions back into resources (or at least cards), so he can recoup his costs faster. Alchemical Transmutation is a strong combination (provided you have the for it), and Decorated Skull and Burglary are at least situationally useful.
I think the basic principle in play here is that extra actions are generally weaker than optimized actions, and those are more easily achieved with other cards.