Earlier quoted context omitted.
My last 2 vehicle purchases (2014 and 2021) were through internet sales managers. I told them what I wanted, when I was intending to buy, that I had sent the same e-mail to every $MAKE dealership from San Diego to San Francisco, and that whoever had the best offer was getting my money. It was a painless experience both times.
My friend tried to do this with a Subaru and got nowhere. But it was in 2018 I think. Nothing to lose with the strategy, but it is societal economic situation and demand of car dependent.
If you start off combative I think its much less likely to go well.
I just let my fiancée know recently that this is how I intend to purchase our next vehicle. Strictly through email until the day I go to pick it up in person. If they say 'You have to come in' to talk price I am going to hang up immediately and call the next dealer on my list.