Google "what did theranos do" to find out why.

It is largely about insurance reimbursement. Your health insurance won't likely cover something the FDA hasn't cleared.

Because tests aren't completely innocuous? Because tests lead people to make significant medical decisions?

Look at the supplements world, where grifters are shilling chemicals that cause harm and make radical claims for absurd markups. Or gas station pills. You want those companies making Alzheimer's tests? People going in to a 7-11 and buying a "all illness test card" that tells people they do or don't have degenerative diseases?

No, it's very very important to ensure tests are actually indicative and ensure they are well made. To do that, a regulating body needs to be involved.

I think you need FDA clearance to be able to market a test as actually being effective for treatment/prevention etc. For exactly the same reason woo-woo supplements must disclaim that they aren't intended for that purpose