DoH and DNSSEC are orthogonal systems. DoH protects the connection from the client to the resolver from eavesdropping or tampering, but doesn't do anything to ensure the integrity of the records reported to the resolver (which still uses regular DNS) and doesn't prevent the resolver itself from tampering with the data. The aim of DNSSEC is to provide for the end-to-end integrity of the RRs so that a client can be sure that the reported data matches the data entered by owner of the domain. This is essential for protocols such as DANE. The introduction of DoH does not eliminate the need for DNSSEC and the two protocols can be used together.
At this point, I'd say DANE is more essential for DNSSEC than DNSSEC is essential for DANE. But both are solutions casting about desperately for a problem to solve; in DNSSEC's case, for more than 20 years, through repeated false starts in design.
The comparison with DoH is imperfect, certainly, but still probative. DoH does something, today; it protects queries to sites all around the Internet, and doesn't depend on a boil-the-ocean deployment that must occur simultaneously in two directions (from the service operators who must sign their zones and from the end systems which must upgrade and enable DNSSEC). DoH is a relatively young protocol and will, within the next year or two, be almost completely mainstream, a feature of most of the deployed base of browsers. DNSSEC will still be languishing, because we aren't humane enough to drag it out to the yard, rifle in hand, to put it out of its misery.
