This is a cultural and personal preference thing.
In Latin America nobody would question calling her a doctor as they're very much into formal titles stuff like that.
In the U.S. some people with academic credentials such as Jill Biden encourage using Doctor and some don't.
I get why some people take it as pompous but why people think this is any kind of big deal doesn't compute to me.
Except if you hate the president.
That doesn't seem to me a good reason to make a big deal about Jill Biden's title.