Instead, at the start of a treatment on a patient, an analysis must be done of all available data, and the treatment only allowed if the error bars put it within the realm of the best treatment available.
That means at the start when not much data is available, it is easy to give it to a patient. But over time as more data comes in it gets harder and harder to do so if the treatment is ineffective or harmful.
Data should be collected and analyzed in real-time - it should be a matter of hours between some life event like a death feeding into the dataset used for decisions on new patients.
Biggest example of this risk aversion is the peptide craze going on (the most famous of which are GLP-1 antagonists). It's pretty much a wild west where people read a low-sample animal study, and buy a drug that's "for research only, not for human consumption" off of a compounding pharmacy in China.
Few human studies because even if you have willing and enthusiastic volunteers it's too expensive and creates legal liability. And the FDA cannot approve it without a high bar of evidence (for effective treatment and low risk) and costly, time consuming reviews. Because of this, there is a black market for the things and people are basically being their own test subjects.
This may be true, but I don't think it's the major driver of conservatism. Two thoughts/observations:
1) Bodies like the FDA face a strongly skewed set of incentives. If they take a risk on something and people get hurt, they face huge public criticism. If they take a risk on something and it's all fine, very few people care or notice. As such, they are strongly driven to not make a public mistake - which drives ever more conservatism.
2) FDA can actually be innovative compared to other health authorities. Breakthrough therapy designation, Project Optimus, Project Frontrunner, and others - show this. However, they've got a strong 'not invented here' mindset - they flatly refuse well-meaning individual innovations from pharma companies, if they're not compatible with FDA's guidelines. And they're heavily bureaucratic, meaning the innovations that do appear are usually following years of process (which probably links back to #1).