Pwned Passwords[1] is just such a database (with passwords hashed using either SHA-1 or NTLM as an obfuscation measure, and without any emails). Hunt used to distribute versioned snapshots, but these days he directs you to an API scraper[2] in C# instead, so you can still get a list but it probably won’t exactly match anyone else’s.
This isn't sufficient for all cases. For example a breach could contained a hashed passwords. If you only have the obfuscated passwords of previous breaches you can't hash it yourself to know that the new breach is just a rehash of an existing one.
Data breaches can also contain other things than just passwords. Things like phone numbers, addresses, etc that would also be useful for checking.
Publishing someone’s leaked credentials in plaintext for anyone to look at also isn’t ideal. I mean, yes, it’s been leaked, but we also don’t need to make it easier for someone to get hacked.
[1] https://haveibeenpwned.com/passwords
[2] https://github.com/HaveIBeenPwned/PwnedPasswordsDownloader