Relevance presumably increases p(click).
"advertiser's ability to pay" has no bearing on things. If the advertiser does not pass credit checks, it doesn't even enter the auction.
There also is clickbait.
Search Ads are pay-per-click (or conversion now? Not sure)
All others are pay-per-impression.
conversions are what the advertiser really cares about, but they're hard for Google to be sure about. And what if you see the ad today but buy it next week in the store?
Organic search? Corrupted by SEO, so not neutral. The advertiser's ability or willingness to pay, is at least something of relevance? It reveals at least someone has the product you want, and possibly a deal.
You can read about how it was in 2008-10 here:
https://albertcory50.substack.com/p/working-at-google-ads
Undoubtedly it's different now.
p(click) is an estimate, of course, but you'd reasonably expect that Google has gotten pretty good at that.