I posted a similar question here[1].
I'm not a GOPer, but I do hold some fairly free market beliefs, so I wanted to answer your question about the general case. I think some of this thinking comes from the fact that there's been a lot of legislation in the past that attempts to solve market "failures" with more government regulation or subsidies, and that those promises have fallen short. In my mind, there are a lot of liberals in the US who say things like "if only the stimulus was larger" or e.g. after the "assault weapon" ban failed to demonstrably change gun violence in the US that we "just needed to ban MORE guns".
For me, the big one on this is healthcare. I'm the first to admit that a single-payer healthcare system is my 2nd favorite system after a purely free market approach, but there's a lot of gaslighting going on that what we have today in the US is actually a free market approach. Liberals tell me that the free market failed, and that it's time to socialize healthcare. But from where I'm sitting, we've had massive governement intervention in healthcare for a century, and that intervention has made the market aspect of our system fail completely, govt subsidies for employer-provided insurance being the number one (inflates prices by increasing demand for lower-pri care, ties people to their employer for longer than they'd otherwise do), but also Medicare/Medicaid and the lack of insurance pools across state lines.
This debate falls out most cleanly when you debate the Laffer Curve. Are we on the left of optimum, or the right? There's really no way for us to know for sure in a vacuum, but "doubling down" is the only approach that either side can really take in pushing increased or decreased tax rates.
Obviously, I didn't flesh out all my positions here, and I don't mean to get into a debate on any of these things in particular. I'm just trying to help explain some of my own logic in response to your question.
[1]: https://news.ycombinator.com/item?id=27778374