The rest stroke has nothing to do with thumb or any fingers any more than free stroke, so is irrelevant. But - it's much more difficult to achieve, especially for beginners, so isn't so commonly used.
If the thumb made for faster, better playing, players would be using it more. Fingers actually are better for this - all in the same plane, and physically more similar than the thumb.
Thumb, in classical playing, being more fleshy, produces a softer sound, and thus is often used for the accompanying bass line or arpeggiated chords, usually on the lower strings.
Having said all that, using apoyando, or rest stroke, surely won't work on fast passages, as there's literally no time to rest. So, do away with that for now, try to use much less thumb - that'll set you up for later stuff - and get used to using at least I and M, and certainly introduce A into the party. It might just help to consider the classical guitar as different in many aspects from the electric, and indeed, the acoustic guitar. As one probably would considering a bass guitar, for example.