If you can trust the provider, why use an expensive blockchain instead of an inexpensive database?
Because the amount of trust required is significantly reduced if the provider uses a block chain. Without a block chain you need to trust that the provider will not change transactions retroactively. With a block chain you only need to trust that the provider will not censor transactions.
Sure. A centralized chain can be used for anything that a decentralized one can be used for (with one exception [1]), you just have to trust the provider.
[1] The exception is that a decentralized chain cannot be used to fairly distribute rewards to the participants in a decentralized protocol. That makes it harder to use a centralized chain as money because you need a separate mechanism for controlling the money supply than the one that maintains the ledger. In a distributed chain, the same mechanism serves both purposes.