To answer the question of whether government participation into research is good, I think one way to get at it is to answer this question: would Elon Musk and his endeavors be better off with or without government funding? I think Musk is a good case because he epitomizes private entrepreneurship yet also receives government aid

Musk was in debt, on the brink of losing everything. The first two SpaceX launches failed. If the third failed, they'd have to close up shop and Musk's other businesses and personal finances would be in ruin. The third launch succeeded and the government gave SpaceX enormous contracts as a result.

This suggests that Musk was saved by government funding. But I contend that isn't the case. Musk's success is determined by other factors. His turnaround was ultimately due to that third launch succeeding. Only then did the government give life-saving contracts. But what if the government hadn't jumped in, and likewise what if the government didn't jump into any other markets? Would SpaceX be doing as well today? Perhaps. Without government intervention of any sort, Musk wouldn't have been on the brink of bankruptcy in the first place since he would have had more capital due to lower taxes. Private investment from others would also have been higher since there would have been no crowding out from government investment. However, that doesn't make the case that SpaceX would be better off without government funding.

But we're not talking about SpaceX, we're talking about Musk and markets as a whole. When just about everybody discusses markets, we tend to gloss over that aggregates are essential, and we forget about unintended consequences. Now we have to talk about Tesla, also owned by Musk. Tesla far exceeds the competition in virtually every aspect, yet that competition doesn't feel the full brunt of this because the government has propped them up like crazy (think: auto bailouts). It is likely that if the government hadn't saved the auto companies, there would have been a much greater natural shift towards Tesla. This, I think, would have put Musk in an even more powerful position than he currently is, and this means that even without government funding for SpaceX, he would ultimately be able to raise more capital for SpaceX. It's like how Bill Gates can raise just about as much capital as he wants because he has proven himself through Microsoft. Musk would have done the same thing with Tesla, but didn't because government incentives pushed for a different direction.

TLDR: Government involvement made Musk expend more effort into SpaceX than he probably should have (chasing government funding), and made it harder for Tesla to kick the competition's ass (government propped up the Midwest companies)