This is not a problem unique to stablecoin providers. Every company with a large number of stakeholders (e.g. public companies, bond issuers, companies that manage assets on behalf of their clients, etc.) faces the same problem.
The traditional solution to this is to have a widely-trusted third party, like a big four CPA firm, examine the company's books and operations and provide an audit. It's still possible to defraud auditors (there used to be a "big five CPA firms" before Enron blew up and brought down Arthur Andersen, and more recently Wirecard made EY look pretty bad), but it's a lot harder than defrauding people who don't get a detailed look at your operations. The reason to go with a big four accounting firm is that the firm's reputation with the public is substantially more valuable than any particular client relationship.
All of this stuff has known solutions, but people don't like what the solutions would show.
USDC seems to be doing it just fine?
https://www.centre.io/usdc-transparency
> Top five accounting services firm Grant Thornton LLP issues attestations each month on the US dollar reserves that back the USDC tokens in circulation.
On the other hand, it looks like USDC's market cap doubled in less than two months, so I guess that's good for them?
[1] https://news.bitcoin.com/usdc-attestations-run-late-raising-...
It’s odd that cryptocurrency was designed to work without trust and yet many people are so trusting.