A good patina will contain a good chunk of burnt oil, it’s not that the stuff vanishes when smoke gets produced linseed oil in fact produces very little smoke compared to say canola. Never getting to the smoke point of whatever you have on there will result in a non-black and not entirely unlikely also gooey patina.

It’s not a good idea to go miles beyond the smoke point but hovering around it is pretty much optimal. You use oils with higher smoke points if you want a more aggressive sear without ruining the taste of whatever it is you’re searing, the thin layer you smoke off when heating the pan, or that smokes off while the pan is cooling off quickly after adding oil+ingredients, is generally so miniscule that it doesn’t really affect taste short of giving some wok hei which is generally a good thing. If the smoke alarm goes off or you need to open a window you’re overdoing it.