In the broadest of terms, medical degrees, MDs, are ultimately for people who want to help patients. Jokes about pathologists aside, the majority of medical do want to see people on a personal basis and heal them.
Now, modern medical programs often have research components; usually small ones, and MDs of course participate in research, but the vast majority do not perform any once they are licensed. If they do, it's often as the person who arranges the treatment, whatever it may be.
As other people have said, PhDs are to train you to do research. Outside of psychology, they don't have patient contact. So if you want to do research in the life sciences, but don't want to practice, there is no reason to get an MD.
That makes me wonder: why bother getting a PhD in say, immunology, when it appears that an MD is objectively better. With an MD you are qualified to run a lab despite not having the terminal degree of a typical researcher, ...
A fresh MD is less qualified to run a lab than a fresh PhD. Of course, fresh PhDs don't get labs anymore, but a PhD + postdoc is much more qualified to run a lab than an MD who has been practicing (not researching) for an equivalent time.
Of course, an MD could play their cards right and end up on a research track, but medical school isn't shorter. Medical school + residency is longer, and much more difficult than PhD school + postdoc.
To me this seems like the 5+ years spent becoming an expert in your field by doing novel research doesn't really matter as you can get a research job with an MD that doesn't require any of that.
That's not what happens: MDs have to add in research on top of what is already a difficult professional training program. And, often, they don't do it well. I don't want to speak in general terms, but I dislike working with research MDs: They are supremely busy, and are less present in the lab because they are in clinic multiple days per week.
... and you are trained as a physician or whatever specialty so you always have something to fall back on.
While true, you have to maintain your licensure, so add that on top of a busy research job, and doing that looks less attractive.
While you say "fall back on," a practicing physician in almost any specialty is practically guaranteed to make more than a PI in the same field. My last PI was an MD (and one of the reasons I dislike working with them), and as a senior neurologist, probably could have made double in practice in a hospital or privately.
So if you want to do research, why get a degree that would get you more money elsewhere, and take out a loan to do it? PhDs are paid to go to school, even if it's a pittance, and do not take out loans for tuition. MDs must.
Finally, as others have pointed out, keep in mind Dr. Fauci is old, and is from a different time.