That's no excuse. KeePass allows having the database file locally where it's you duty to manage it.
It might be less convenient, maybe. But I don't see valid excuses for people to not start using a password manager, even less the less tech savvy people.
There’s also the possibility of mismanaging your password database and losing all of your data.
Is it, really? And at the same time to trust one's memory? For memorizing hundreds of long passwords? Don't think so...
There are alternatives to programmatic password managers or human memory, e.g. a paper notebook and a safe. That's not an approach I would personally take, but I imagine it's a reasonable option for someone who sees the potential danger of trusting any program for sensitive data.
The alternatives are same password everywhere or keeping a paper around with the passwords written in plain text. Both are equally disastrous (unless you work at home and don't ever get robbed)
KeePass is open source. You can review the crypto, or pay somebody competent to review the crypto, or trust that the project or some 3rd party has done so.
I wouldn't go out of my way to publish my KeePass file publicly, but any attacker who can break the 256 bit AES encryption, or brute-force/dictionary-attack it's key that's using Argon2 KDF with enough rounds to take 1 second per key transform on my laptop, is well into the "I stand no chance against state level actors specifically targeting me" category, and I'll just assume I've lost to them already. In the immortal words of James Mickens: "If your adversary is the Mossad, YOU'RE GONNA DIE AND THERE'S NOTHING THAT YOU CAN DO ABOUT IT." If ASIO/CSIS/GCHQ/GCSB/NSA want access to my accounts, it's unlikely having passwords that are only in my memory is going to make much difference to my personal outcome. If a driveby teenaged script kiddie hits a zero day on one of my devices and pops my KeePass file, I'm not even sure I'd bother changing the passwords.
I'm happy enough storing the KeePass file on my (encrypted) laptop hard drives. I'm OK with using iCloud to sync it to my phone. I'm fine with it being part of my regular TimeMachine backups to a pair of external usb (encrypted) drives, and for a copy of that usb drive backup to be synced to an encrypted S3 bucket.
