Why aren't those types of clinical trials, enabling faster iteration speed, moved to countries with less strict regulation?

In general, drug companies do not send employees out to inject patients with drugs. That's not how it works.

Instead, they work with specific doctors at local clinics who treat patients. Those doctors agree to fill out appropriate documentation (and are paid to do so) which the drug company then uses to submit to the FDA/EMA to get approval for sale. Those doctors are considered Principal Investigators, in that they are fully responsible for patient treatment AND for reporting patient outcomes to the drug company.

All countries with sufficient, local medical expertise, also have regulations on how trials are conducted. Those regulations are different from US/European regulations, and unless you're an expert in, e.g., Chinese clinical trial regulations, you have a very steep learning curve.