the championship money is also pennies to the teams

The constructors championship money is absolutely a massive impact for the teams. Last place (11th) is estimated at ~$50 million, 5th place is estimated ~$100 million, and 1st place ~$140 million. For a team like Williams or Haas, every position they move up the ranking makes a substantial budget impact (both of those have estimated total budgets ~$230 million). Even for one of the big 4, with budgets in the $400 million range, the $40 million swing from 4th to 1st is not insignificant.

Heck, Otmar had to pay his staff out of his own pocket back in the day (I don't remember what cost-cap was in place back then - I think that was during his time at Force India). Those lower teams are more stable now that 20 years ago, but still struggle to get enough sponsor money to compete.