Interesting question! I've been in government contracting off and on for over a decade. I've spent the last 5 or so helping small businesses get contracts and grants. In my opinion, having a 2 sided business - 1 for commercial and 1 for government - is a very good business strategy. But it's hard finding the right people to join the team because we get snatched up by the big shot military contractors all the time.
To answer your question, it is a very common way to start a startup in big government contracting towns. I see that all the time around here (SE US). Government contracts have been spinning up new tech since I've been in the business. But there are high barriers to entry for new players, unfortunately. Most of them have already been discussed already.