What you describe is the present condition.
No, now you have many private groups with slightly different interest temporarly unified. Once you create one gigantic mega contractor, that group has a much more specific and target interested in lobbying for that one specific program.
In other words, no worse than the present condition.
But it would be increasingly awkward for Congress to be seen to force NASA to choose the $2B launcher from vendor A over the $10M or $50M (or whatever) launcher from vendor B.
No, what happens is that you create a seriously powerful group of private institutions that will go full force into lobbying congress to not kill the project. Even more so then now.