The best estimate I can find is that about 3.5 million people in the US have a PhD or another research doctorate. That includes non-immigrants who study or work in the US. According to AAUP statistics, there are ~200k full-time equivalent tenured or tenure-track faculty in what they consider doctoral institutions. Such positions are the typical but not the only option for a research career in the academia. The numbers are well within the parameters I used for my estimate.
It's important to understand that in this context, willingness to relocate means willingness to spend your life outside your home country. Even in a large country like the US, there are often structural reasons why universities are not interested in hiring someone like you when you are in the job market.
For example, maybe a field such as ML starts getting popular. Universities respond by hiring new faculty, who in turn hire new PhD students. Almost a decade later, when those students have graduated and are in the job market, the demand may have stablized. Universities already have a plenty of faculty in that field and have little interest in hiring more.
Which means that if you chose a popular field, your chances of getting hired may be below the average. If you want to stay in the academia, your best bet may be moving to a country that didn't experience a similar hiring frenzy and is now trying to catch up.