No, you don't get it. There are ALREADY too many coins. Slowing the flow of them doesn't do anything about that problem.
As for the publicity... yeah I doubt too many people at a nascar race are going to give 3 shits about "doge." Besides, my point is that if you set aside opinions and look at the facts, the price hasn't increased when each of these big publicity stunts has happened, not the recent ones. The bobsled thing had some impact, now no one cares. You can't possibly think a freaking NASCAR event is bigger than the olympics, can you? The olympics sponsorship was a much bigger deal and the price still kept dropping.
The price manages to be stable (actually, to raise) even though there are "too many coins". That means there's more buy support than sell resistance. Slowing the flow of new coins to instant-dump multipools will decrease sell resistance and thus a price increase, or at least stability, is quite likely. A coin being "rare" means absolutely nothing; look at the mess that 42coin is.
The impact that publicity gives is long-term. Someone won't buy Dogecoin after hearing about it once. But, if he hears about it enough, then makes research to see it is legit and supported by an amazing and active community, and that this community is ready to invest around Doges in many different and creative ways, he might.