It’s funny, first think I thought of was what about assists? You don’t have to be dependent on meter, but you could be overly reliant on assists.
Zero is probably the best solo (he doesn’t really need meter or an assist to get in)
Wolverine a close second in my opinion as he’ probably the best rush down character in the game due to his speed and fast normals, but needs an assist after his hard knockdown.
Viper is more assist than meter reliant, she builds about a bar anyway.
Dante, but the slow start-up of his normals leaves something to be desired (he has good mix-ups, but a double-overhead won’t land on high level players too frequently).
Doctor Doom, but he needs an assist more than meter. (S footdive is nothing, from time you can block it crouching)
Trish Forget rushing down, runaway with her…
And, eugh, Wesker…
There’s also Ghost Rider, Doctor Strange, Chun-Li, Iron Fist but are they worth mentioning? I love them, but there flaws reduce their viability.