Practical implications of finality time for L2s

Quite frequently with crypto I realise that I really don't understand what are probably basic issues. I was just thinking about finality time for rollups and whether use cases such as payments that require near immediate confidence or certainty are problematic. I suppose one is splitting trust between the L2 and Ethereum, and so I wonder what degree of trust is necessary for payment applications? Should we expect to see payment processors creating their own L2s so that they're fully liable for transactions until a proof is submitted?