Sure his handouts keep things stable and he can pave the roads, but he sets himself up as dictator with no plan for replacement or succession. It's notable how literally all the options but Huey for the AUS are total shite; Business Plot are cartoon villains, Pelley is insane, and Earl is completely incapable of matching Huey's modicum of competence.
The business plot and Pelley are not even considered sucessors for Long; the first got purged if they do not manage to coup Long fast enought, something that happens most of the time; the later is even more unlikely since the own description of the event of the american legion says that the door is closed for Pelley so the player really must want him in power for Pelley to rule america. Furthermore, Pelley different from Moseley does not tries to coup the government of the AUS if you leave him alone and Long still purges him with the Destroy the Klan focus. To quote the tvtropes wiki:
"The leadership of Long after his triumph is very similar to the Brazilian populist president-dictator Getúlio Vargas. Thy are both authoritarian populists who allied with far-right elements against socialists and moderates in a multilateral power struggle for control of their country. Like Vargas, Long will purge the far-right as soon as their mutual enemy is defeated."
Now for his ingame possible sucessors, the event of the businness plot tells us a bit about the lore and how Long appointed his wife as sucessor, like Perón appointed his wife Isabel Perón as his VP. Earl get's power only if Huey is killed by Moseley and this ends being discovered. Since the gameplay most dies by 1948 it is quite open to find who would be the sucessors of Long, and because of that someone made this list below on the reedit:
Now imagine a sucession of Huey Long to Lyndon Johnson, that would be a ideal scenario.
Edit: I took a while to answer because this image was very hard to find.
Also, on the CSA route if you pay attention some events talk positively of Huey Long and his family, even with they being exiled. I don't know the right event to fire it and post a print but it is about Francis Townsend.