Three cars per team isn't a problem if the underlying points/prize money system is overhauled. The simplest idea being that the teams only get points from two cars towards the constructor's title, but the drivers each get points for their championships. Thus the teams get the same money as today.
Better would be points all the way down the grid, not just the top places with "points = £" at the end of the season. If a team can't afford three cars then its points are adjusted 3/2. Of course, three cars gives better odds of having point paying finishes which does give an advantage for the three car teams over the two car teams. Put a cap on prize money, however, so that the top teams don't get to take it all - say, £50million allowed from prizes. That gives a better spread of money to the teams.