1. for PoW to discourage motivated spammers, the difficulty has to be high enough that it significantly affects UX for earnest users with low end hardware afaict (ht: adam back)
  2. API providers can't earn from PoW
Obviously, lightning payments are on par or worse UX than (1) right now, but there's at least some hope it can be improved. Lightning payments of this type are also more likely to be widely adopted given (2).