This already happens for tx fees automatically in the background, your client picks the cheapest route. But this doesn't happen for LSPs because switching LSPs requires an on-chain transaction. I agree that this will be a cool feature to have eventually, when people may be connected to multiple LSPs, IIRC zeus supports multiple LSPs at once.
Discussion
True, I was thinking more "pay as you go" structure.
But at the end, I could also argue, that starting with a custodial solution to get understanding, then moving to non-custodial is also a good path. Because maybe making such solutions might sacrifice something important.