Tracking somebody from clicking on the ad, through to the purchase doesn’t prove that the ad added any value, though. The ad only added value if the person wouldn’t have otherwise found the product.
I think this is more of an effect for things like search or ads on an e-commerce platform (somewhat ironically the contextual ads people here are advocating for are much more susceptible to this) but less so for a lot of the more random ads, especially for niche products.
Edit: For me they are obviously effective. I think the more interesting question is exactly what the return on ad spend generally is but that would take very specific data that I don't have access to.