I was on lots of anti-biotics as a kid and I turned from skinny to fat at some point. We know already from experiments/treatments being made that fecal transplants can make a fat person skinny for example (no I didn't do that :))
Personally I transformed my life from being very lethargic and not being able to tolerate anything but small amounts of certain foods and also alcoholic beverages without getting major migraines by getting the right probiotics. To give you an idea, eating leftover lasagna two days in a row was a sure fire way to get a migraine, as was drinking a bottle of alcohol-free beer and anything with alcohol was even worse. Even just small amounts. We're talking migraines where you feel like you're gonna puke and my eyesight was affected as well.
I felt really sick for about 2 weeks after starting the right probiotics. And it wasn't just any probiotics that would do. I tried out different ones, until I found a specific one that mainly differs in one bacterium from all the others I tried. Bacillus subtilis in case you're wondering. During that time my then current microbiome would've been fighting with the newly introduced strains. After that, I was no longer lethargic and slowly but surely I was able to tolerate foods in normal quantities again. Leftover lasagna is just awesome now, like it should be!
So yeah that's just a personal anecdote on how gut health can really eff up your life and health. So I can very well believe that people with a 'broken gut' would die more easily from COVID or get infected more easily with other things as well. But where's the money in simply fixing peoples guts? Isn't it 'better' if we make them sick, so we can then prescribe them stuff?