No, DNSSEC tries to solve one part of the security of DNS (security of records between resolvers) and does nothing for the security between the user and their DNS server. And doesn't even do a good job at the bit it tries to solve.

It should, though it achieves that goal by a chain of certificates not unlike CAs just tied to DNS. Like I said, it essentially just moves the problem.

Which might still be better, if only because it limits the surface area.

DNSSEC deployment has been anything but trivial. This APNIC post from 2024 estimated that about 1% of DNS queries were being validated via DNSSEC: https://blog.apnic.net/2024/05/28/calling-time-on-dnssec/. That's more than 25 years after the IETF first standardized DNSSEC.