It’s a real shame that there is no independent, good, engine manufacturer. Sold to a majority of teams. Then a team like Haas could prove themselves with their construction skills, or not.
There will always be teams that are the complete package, i.e Ferrari, or Mercedes, but I don’t think that supplying other teams adds to the racing potential of that other team. The works team will always be better than the teams it supplies. I’d go as far as saying I don’t think it should happen.
I am not sure it would make an ounce of difference. The huge gap between the top (Ferrari/Mercedes/Red Bull) and the mid-field has almost nothing to do with those teams being supplied inferior engines to the works teams (if that happens at all). The difference is pretty much all determined by the aerodynamics/chassis. Put differently, the mid-field are already massively losing the battle in construction skills. This is mostly a matter of budget.
With that in view, it makes very little sense for the engine manufacturers to supply inferior parts to their customers. It makes more sense from a QC point of view to make all engines to exactly the same specifications. There might be some natural variation in the process with the works time getting the first pick, but I highly doubt there is much of a difference to made there. (Unless a manufactures is facing a shortage of parts, i.e. Renault at the end of this season.) Anyway, this could easily be evened out through the rules. (New engines are to be supplied to the FIA in lots of 6, whenever a team (works or customer) needs a new engine they are assigned a random one from the lot.)
The main advantage gained by a works team is that engine and chassis can be developed in conjunction leading to both being better adapted to each other. However, this advantage is lost in any other supplier/customer relation whether or not the manufacturer is running it own team or not.
It seems to me that the often repeated "F1 needs an independent engine supplier" trope, is mostly a piece of Red Bull propaganda. Red Bull's interest is to minimize the potential for performance differences coming from the engine, because it plays to their strength: aero. However, when you look at it more closely, there appears to be little merit to the argument.
Finally, note that the fact that Red Bull is 5-2 vs the Renault works team in seasons that Renault supplied Red Bull and operated its own works teams is clear evidence that the "The works team will always be better than the teams it supplies." is simply false.