Approval ballots is just a special case of ranked ballots with only two ranks, so as far as considering and honestly rating a large number of candidates is concerned, it shares any problem ranked ballots have.
While there are some good arguments for allowing ties in ranked ballots (unforced vs. forced preference), I think there are pretty big problems with forcing tied rankings.
> If it can handle proportionality almost as well as single transferable vote
I don't think it can, but because there is no clear mapping between actual preferences (or preferences that would be provided on an unforced preference ballot) and approval ballot (or any other limited-rank-preference ballot) markings, that's a hard empirical question that's not really analytically addressable.
While there are some good arguments for allowing ties in ranked ballots (unforced vs. forced preference), I think there are pretty big problems with forcing tied rankings.
> If it can handle proportionality almost as well as single transferable vote
I don't think it can, but because there is no clear mapping between actual preferences (or preferences that would be provided on an unforced preference ballot) and approval ballot (or any other limited-rank-preference ballot) markings, that's a hard empirical question that's not really analytically addressable.