I think car salesmen are particularly pushy about it because car manufacturers are starting to sell monthly subscriptions for things in the app. They can't sell it to you if you won't install the app. For instance, my Toyota came with some kind of trial subscription for a remote unlock/lock and GPS location service. Served, of course, through the Toyota app. They have an incentive to get you to install the app that goes beyond just not thinking it's a big deal.
Email I got today:
> Your access to Safety Connect and Remote Connect services will expire unless you access your Toyota app or call 1-833-914-0992 to extend your subscription. For as low as $8.00 per month, you can enjoy the convenience of Safety Connect or Remote Connect. For further savings, you can choose an annual plan.
I won't be doing that, but it makes the reason for the push to install their app starkly clear.