F1 team mechanics, principles, and drivers wear apparel covered in logos because those logos are how they pay the bills.
Another income stream is selling that same apparel to fans, making money from the sale and convincing people to act as human billboards for petrochemical companies, boring corporate tools, and the new generation of addictive products under the guise of supporting a team.
Despite the USA being the capitalism centre of the world, with advertising being a cornerstone of the American dream, there are no sponsors on jerseys in the NFL, NBA, NHL, or MLB. They make up for it though; if you ever attend an NHL game you'll probably see a face-off before the puck is dropped essentially frozen, waiting for TV to come back from a commercial break.