This does not make the picture better.
Here are two models of production:
1. You mostly make the thing yourself and pay the R&D + production costs in-house (i.e. public sector). There is little to no profit-waste. You need the thing, and so you created the thing. In this case, you are aware of the personnel, R&D, production costs. AFAIK this was mostly the state of play during WW2, or at least a lot more common.
2. You notify the market that you want a thing, and pay a profit-seeking vendor for the finished thing. You need the thing, so you bought it. The price breakdown beyond the product itself is opaque. You should not need to be aware of the personnel, R&D, production costs of BigContractor Inc. Does it actually cost $40K to produce a trash can? Fine, then that+profit will be the lowest bid.
You are describing a corrupted third model, where you essentially manage the entire production process, but also give extra money (profit) to a third-party. To say nothing of the massive waste of involving unnecessary middlemen.
This third model may or may not be how the government actually procures stuff, but again, it does not improve the picture of enormous government waste here.