The website URL sounds like a good idea!
I think there should be some official guidelines set for what information should be shown on the front page of the pool operator’s website. It’s a guideline, not a must, but it would hopefully influence people who stake with the operator.
Such as company name, address, registration number, tax number, full name of owners / major shareholders and maybe quarterly / yearly financial reports, Customer Support Number / Email with SLAs provided (and corresponding reports), security audit reports, staking performance reports (number of delegates, staked ADA, costs, profit, reward, etc.), incident reports, staking node infrastructure characteristics (cloud or on-premise, geographic location, HW capacity, etc.).
The increased publicty and insight of operations of stake pool operators brings a Proof-of-Reputation flavor / nature to the Proof-of-Stake protocol. The owners / major shareholders have their reputation at stake to provide a good quality service for the pool.
IMO transparency & good quality of service is highly desired for pool operators and proper incentives should be put in place.
I would personally even not mind in this context if a 50+ reputable Nasdaq companies (selected & invited) would operate pools as well along the Community pools to have a nice mix.