You loose inspection, export, replay and audit.
None of the popular providers have real moat, which is very much problematic for OpenAI and Anthropic; their operating margins are deeply red and they do not have the same reserves that FAANG/MANGA has. FAANG/MANGA does the same to kill fair market competition in the long run.
This is one of the ways in which model providers are attempting to artificially create moat where there is none.
There are only functional objections to this.
This is fundamentally antitrust material. However, this is “acceptable” in contemporary USA because the FTC has been gutted to follow Trumponomics.