If Fultz is so great though, why doesn't his team do better overall? I have to be somewhat wary of a player on a mediocre team
I agree but it did not stop Ben Simmons from going one.
Washington has a really young roster of players that primarily weren't highly rated (compared to players at Kentucky, for example) coming out of high school. 10 of their 14 players are sophomores or freshmen. Furthermore, they had two kids blow up enough last year (Chriss and Dejounte Murray) to leave after their first-year, further depleting their talent. As far as the PAC 12 is concerned, they're in the lower half of talent, excluding Fultz, and very young to boot.
Now it's fair to ask why Fultz went there, but when he committed, Murray and Chriss were going to be there too, which could have been a really nice team. Once those two went one-and-done, the team was obviously worse off. But if the coaching staff could turn someone like Chriss, who was outside the top 50 coming out of high school into a top 10 pick within a year, that might not look bad to a prospective recruit.