I am mostly of the "The GOP's structural advantages and rock-hard loyalty of the base give means they have no incentive to get less crazy" view, but I think that Doug Ducey's collapse in JA numbers under COVID is a good look at the alternative view.
Ducey won reelection by a double-digit margin in 2018, in a year when Democrats won a bunch of statewide offices in Arizona, including the Senate seat. He had the reputation of being a staunch conservative, while being relatively competent and very business friendly.
Over the course of 2020, he was extremely indecisive when it came to fighting COVID. The state kept having outbreaks, and Ducey often responded with some too-little/too-late responses—curfews, limiting capacity, etc.—not full responses of blue state governors.
Ducey's job approval absolutely cratered, making him one of the least popular governors this year. But what's interesting is that some of the fieriest denunciations I encountered were not by Democrats or folks upset about COVID deaths. It was Republicans. https://www.azcentral.com/story/news/politics/elections/2020/10/02/arizona-gov-doug-ducey-viewed-favorably-35-voters-poll-finds-suffolk-university-usa-today/5886892002/
As someone living in a pretty red area of the state, I encountered many who thought he'd gone crazy, and was catering to the radical left. All while doing one of the more timid responses of any of the biggest states.
Would Ducey have been more popular this year if he'd just gone full steam ahead in shutting stuff down? Or if he had just taken the Kristi Noem approach and said everything was fine? I have no idea. But his split-the-baby approach seemed to piss everyone off.
Arizona is a state with a GOP that has become increasingly radical in recent year, with the state party soon voting on whether to censure not just Jeff Flake and Cindy McCain for supporting Biden, but Ducey himself for not saying the election was stolen. https://www.12news.com/article/news/politics/ducey-flake-cindy-mccain-arizona-gop-plans-to-censure-leading-republicans/75-4bb4d1c5-a3d9-45be-b65e-99c614f4f4cc
Chances are that in 2022, when Ducey presumably runs for Senate against Kelly, he'll have trouble winning the GOP primary for that seat, jeopardizing R's perhaps best chance of taking a Senate seat.
Does this mean that the AZ GOP will suddenly go back to normal once they realize this isn't working? Probably not. I think the most likely outcome is that things keep getting crazier. But it's still a clear case study of how it's basically impossible to be an R in a bluing state.