After years of contemplating, I once tried going after an SBIR with a partner. It was for a robotic ship tank inspection system. We put a lot of time and effort (about a month of constant work) into designing a strong concept solution and puting the proposal together. However, we had a few basic questions and the government technical and programmatic POC on the solicitation was non-respinsive after several contact attempts.
We submitted our proposal, meeting all of the insanely meticulous format requirements, but as feared we never recieved a response. Instead, the award was given to an off the shelf product for an incremental upgrade. Clearly, the awardee was already identified by the PM before the SBIR solicitation was even written, so I essentially lost a month of my life by being mislead into thinking the solicitation was truly open. The SBIR was just another way to funnel R&D money to the existing product the PM manages.
Gov't PM's do this because government funding comes in "colors" that specify by law how the money can be used (e.g. Operation and Maintenance, Construction, R&D, etc.). However, for some programs it's hard to secure R&D dollars, so back channels, like working with your supplier to craft an SBIR solicitation you know you will be awarding to them, are needed to fund improvements.
I suspect the fear of this occurnace (wasted effort) is the primary reason startups avoid government funding, and I can tell you first hand it's a valid concern. If you think the U.S. doesn't have it's own backchannels of corruption and unfairness in the contracting community, and that such practices are limited to developing or non-ally nations, you are mistaken.
Ironically, I think one of the reasons this type of behavior has emerged is thanks to the push from our own citizens - largely due to the "fleecing of America's dollars" scare of the 1980's and 90's, which asked America why the government was buying a $100 hammer or a $200 toilet seat. The push for transparency and frugality has driven the government in many cases to a culture (or requirement) to use funding loopholes and side agreements to get work done and also award contracts to lowest bidders regardless of the quality of the offering.
There are good program managers out there, doing their civic duty and following all the rules to the best of there ability. However, to me, the chance of finding such honest brokers and opportunities isn't great. If you want to work with government, your best bet (IMO) is to go to a trade symposium in your specific area of interest and strike up conversations with PM's in attendance to discuss solutions to their problems.