DNS over HTTPS is being discussed to resolve that problem. The downside is it doesn't really exist yet.
DNSSEC doesn't do anything for query privacy (in other words: most of the reasons you'd use DNS-over-TLS aren't addressed by DNSSEC). DNSSEC is a bad standard whose primary impact on the Internet would be to replace the LetsEncrypt CA system with a PKI run by world governments. That sounds like something InfoWars would say, but I promise you, DNSSEC is weirder than InfoWars.
For now, the right answer is DNS over TLS.