On the surface, it is just as you have described it. But the reality is different.
Every fresh client will go with the lowest rate in his project. And eventually he will be burnt and will realize that the rate and quality go along. In that case, he can try another project with the medium rate or go with the high rates from contractors closer to him. This is where your chances are.
Another case is that clients will chose you over the cheapest rate because of the legal liabilities. He will pay you more, but he is sure he can sue you in case you do the job badly. I doubt he will sue some company 3000 miles away in a country with weird laws. Such clients are your chance as well.
Now, from what I have seen, Western contractors will get hired by clients of their own country and they usually can make a good living with 2-3 clients. Other low-rate contractors must have 100 clients to make the living. Would you replace with them?
So although they will accumulate jobs with the lowest rate, they will NEVER do them with quality. Why? A simple math. They do the job at the lowest rate and those clients are usually assholes who want 1M project for 10 bucks. So low-rate clients will have to have 10 or 20 such jobs to actually earn something. What will they sacrifice? The quality.
So although your pace will be slower in gaining quality, you have higher chance to earn from freelancing. I have seen 100s of low-rate guys disappearing after some time (probably quit on freelancing and found a stable job in the local company).