B teams have been tried before. The concept dates all the way back to the inception of Formula 1 when the major constructors used to sell their chassis to independent teams. More recently, it has been tried with Super Aguri and is still going on with Toro Rosso, Alfa Romeo, Haas, and even Force India. It may have been okay in the 1950s, 60s, and 70s, but is no longer appropriate in my view.
Formula 1 should comprise 13 two car teams which are all independent of each other. The last time that this was officially the case was the 1995 Monaco Grand Prix. Even this is questionable though because Ligier was effectively owned by Benetton, while even in years with larger grids, small teams could, and often did, use parts made by the bigger teams. The latter issue is not a problem in my opinion, providing it is not excessive, but having the entire chassis and/or the majority of the components made by a big team is an issue, as it comprises a team's independence, which is the current situation in contemporary Formula 1.
Formula 1 must be reformed, so that independent teams dominate the entry list, just as they used to, and that manufacturers are severely restricted. I favour only allowing them to be engine suppliers, but Ferrari always makes that rule rather difficult to create in the first place, let alone enforce. There needs to be much more of an incentive for independent teams and the grid needs to be filled. Failure to achieve this is going to make Formula 1 beholden to the whims of unreliable manufacturers and lead to even more dull races, if that's possible.