(1) They have a large number of active ingredients that are not cost effective to manufacture synthetically or isolate
(2) They have an active ingredient that is not yet possible to manufacture synthetically or isolate
(3) The active ingredient(s) are not shelf stable once isolated from the parent product
Lastly, and most importantly, natural remedies are not patentable. This means there is not enough money to get them approved for marketing as a cure for disease.
Never underestimate the ability of our dystopian modernity to do precisely this. Amarin patented a specific variation of fish oil (one that is no more bioavailable than literally eating a fish, just more concentrated), branded it Vascepa, and the FDA approved it.
https://en.wikipedia.org/wiki/Amarin_Corporation
I'm sure there are plenty more examples of this, but this is the obvious one that comes to mind.
I get sinus infections with depressing regularity too, and it's awful... I feel very draggy, like I do the bare minimum just to get by, and they go on and on and on, and then presto, antibiotics and it's gone in a day or two, and I wonder why I waited so long.
I really wish there were some advances in detecting (so you're not taking antibiotics for a cold) and treating them.