i agree with you about refuge from the ads (streaming only and no land line helps me avoid a large majority of them), but i would imagine that a lot more folks than we want to believe pay at least some attention to them and are somewhat influenced by them.
I know that's the theory so let me straddle, be a politician, act like a jerk, waffle, whatever and restate it.
I think the only time ads really matter is when you're dealing with a blank slate or a near blank slate. If you're dealing with an established figure (as Presidents running for re-election always are), I seriously doubt the ability of them to move the needle. And on that note I can at least see how in, say, a House race between two newbies, they might well be decisive.
Just to use one example: the 1988 Presidential election.
Everyone knew who VP Bush was. Everyone had at least some level of opinion on him. Dukakis? Hell, half the country didn't know who he was or where he was even from. So ads in that kind of scenario I can see as being at least more contributing to the final outcome. In an election like, say, 1984, everyone had a pretty good idea who both candidates were because one was Prez and one had been VP. There weren't enough ad dollars to buy enough make-up to transition Mondale into "he wasn't Carter's VP," so Mondale was basically stuck with Reagan making the election a choice between Carter's failed term or his own more successful one.
At the same time, I'm talking forever ago now. I've been very fortunate to not have to have sat through very many of those things, but I'd surmise folks get more "ads" in terms of argument on social media now than on TV. The one that still blows my mind is 1996, when I lived in Little Rock, home of the then President. Neither he nor Dole wasted a single dollar on Little Rock TV (that was a relief), but the local races damn near drove me nuts. The 2nd district was a race between a guy named Vic Snyder (the Dem who won) and Bud Cummins (the Rep who lost). Those dudes ran five-second commercial after commercial at each other, and in October that year it got the worst I can ever remember. EVERY ad between shows was political.
And I never knew who was for what, either. Most of the time neither party put their name on the ads except in small print. For years I kept VHS tapes I made of "Tool Time" with all those commercials, and some would be amusing to see now.
(Side note: one of the best commercials I ever heard was on KARN radio. There was a guy running for office in Arkansas named - I kid you not - Marion Berry. He sort of looked the caricature of Foghorn Leghorn type (think Howell Heflin), but he was a Democrat. Whoever was running against him - I think his name was Dupree or DuPwee or something like that - he had a radio commercial where he had Berry standing up as an eight-year old at "Show and Tell" and saying in answer to the "what do you want to do when you grow up" query, answer with, "I'm gonna be a career politician." He then repeated it in Southern caricature of Berry as an adult with a thick accent. Berry won, but the commercial was absolutely hilarious, to the point I nearly drove off the road the first time I heard it).
I just don't think that in most races they flip votes from A to B. Also - the overwhelming majority of TV ads I've ever seen don't really do much except tell me that if the other person wins, I'm going to die.