That's what Sor does, according to his Method. But he also mentions "sometimes" alternating index and middle on the first string, but never the others. He seems to keep thumb/index alternation for the rest. So, when things get too fast for one finger, there are options. He also mentions using hammer-ons and pull-offs for speed, though he doesn't notate this in his scores.
So, we can interpret his works with a modern technique, ignore everything he says, and still make nice music. Or we can attempt to play the music as he might have, and he wrote his Method to help us do that. I don't want to appear biased one way or the other, as both approaches are valid. But I do want to pay him the respect of at least considering his technique, try it out. I'm enjoying it so far, but he is not always clear in his writing, and sometimes contradictory. He does mention using the pinkie (little finger) on the soundboard when the thumb is on the treble strings, removing it when the thumb goes back to the bass strings. You can see me do that sometimes. And the pinkie touch is extremely light.
A further consideration is that he played without nails, and some of the techniques he uses are easier without nails, I think.
Here's someone who plays with a similar technique. Hopefully this extract will start at the 5'20" mark, showing speed playing: