There is a theory that miners gain financial advantage over other miners by mining their own transactions and "recovering" their own fees.

The theory ignores the opportunity cost of mining block space without collecting payment for it. Payment of a fee of any amount to one's self is a financial non-event. Failure to collect a fee is a real cost in the amount forgone, as the cost of mining that portion of the block is uncompensated. The actual fee paid by the miner is the opportunity forgone.

There is a related theory that fee estimation tools may be fooled into recommending higher fees than are required. As shown in Side Fee Fallacy this implies a relationship between historical and future fee rates that does not exist, and that all fees are visible on chain, which is not the case.