Pallas I'm not an accomplished pianist, but I'll offer up what I think. OK?
I think our technical threshold is what gives us a "speed limit", so to speak. By that, I mean, we can't play any faster than we've developed, technically speaking. If we play scales, accurately, at 70bpm, but start to hit wrong notes at 80bpm, that's going to be our speed limit until we develop our finger skills, technique. But, since scales are not as complex as some melodies, our scale "speed limit" may be optimistic for a more difficult piece. Granted, it is possible, even common, perhaps, for a player to learn a song, or piece, well enough to play it fast. But that may not translate to the next song.
Personally, I can play some blues based things on the piano faster than I can play scales, only because I've become familiar with those licks. Generally, I play ballads, maybe a few swing-tempo tunes, so speed isn't much of an issue for me. If I wanted to learn to play fast, I'd find a "live, sitting right next to me type" teacher who would tell me how to fine tune my fingering technique.