Formalizing it into development so that it is policy/expectation for failures and crashes to occur may relieve pressure and help re-orient government and funding expectations.
I think that would be hard. Governments are routinely pressed with the "we got poor people but you spend all that money for space" flawed argument. But at least the gov can shoot back and claim that its space program is providing many benefits and it is a well-run program etc
If the public starts seeing multiple test launches failures they will soon start seriously complaining about incompetency, corruption, and politics. Then the politicians will start pushing the engineers to be more careful, avoid risk etc. After you do all that, what do you get in the end? The exact same situation governments are in now lol
Given how politics work, I think its extremely hard-to-impossible for governments to adopt SpaceX methods.
IMO the best approach, ironically enough, is the US recent practise on space launches. Just set up requirements, let the private sector bid for them by using their existing, or developing new rockets. The private sector doesn't have the public to answer off. Not like shareholders also like seeing explosions but at least if you explain them your business and R&D model they would be more willing to accommodate "failed" tests.
The private sector is also much more willing to experiment, adopt new ideas/practises, be much more motivated in controlling costs, launch cadence, maintainability, turn around time etc.
I actually think the old way of national space agencies slowly building new rockets in a 10 year period is becoming outdated. They will have to change their model towards something more like what NASA does, where they set strict requirements and just let the private sector do the hard work. Of course i would also argue that having a national rocket builder isn't a bad idea so that you won't be held hostage by companies of Boeing's ilk.