I would hazard a guess that it's because they seem to flex the budget every single time, which either means really shitty planning by a company that is trying to look competent or excess greed by the administration of said company to make them more money.
Maybe keep the cost plus but then add a tax increase on any executives running those companies/in charge of bidding. Something like revenues derived from government contracts get taxed without deductible and in a separate file from civilian business so they can't do squirrely tax dodging.
I might weigh those as much or more than actual experience doing the job. New company vs old company with shit record? I feel like we should lean towards the new one but that's weak to spinoff/new subsidiary companies from older ones with a trash rep.