How to list all transactions to one address for a certain ERC20 token?

I am hoping to create a website with a single ETH deposit address for all of my clients.

Clients visit the site, verify their public address by signing a message via metamask, and deposit ERC20 tokens to a single static Ethereum address.

(The deposit address for every single client is identical.)

The site checks Ethereum blockchain to see which address has paid which amount at what time... and stores that info in a local database.

Possible?

Bad/terrible idea? (I know this was frowned upon in Bitcoin for privacy reasons early on at least)

Any tips to help get me going?