It just made the example simpler. In both cases it’s centralisation: if it’s the LSP doing the mining, then that LSP can use the bitcoin more cheaply than a smaller LSP; if it’s a trusted accelerator paying miners/pools out of band, then that accelerator can require the LSPs or miners/pools to comply with their T&C before they’ll do business with them. Doesn’t matter in either case if it’s rare and for small amounts. Does matter if it’s common and a non-trivial fraction of block reward.