It seems to me that plenty of publicly funded research ends up simply pushing ideas which are subsequently developed and patented by companies. Perhaps I misread the situation, but that doesn't seem like it's in our best interests

That's why public funding should be directed at under-funded areas, like "processes and drugs that are not patentable".

Or, improve the independence and targeting of the research. For instance, having medical groups, patients associations, etc of X disease invest in research for X through crowdfunding.

Experiment [0] looks like a good example/PoC for this.

[0] https://experiment.com/