I believe that is exactly the case even in most developed countries that even if people are getting vaccinated, it might be going incredibly slow, with different priority groups first getting vaccinated. In particular, it is well-known that in the EU there is a huge vaccine shortage.
Maybe it is not even always that it is a shortage, but the people who are offered to get vaccinated do not get vaccinated, and those who want to get vaccinated do not get offered to get vaccinated.
The countries that seem to have an abundance of vaccines are those who have received vaccines both from Russia and China, for example the UAE, Serbia, and so on. I read that tourists have been getting vaccinated in Serbia, and apparently it is possible in Russia, but at the same time as far as I know Russia does not issue visas. So I am wondering what experience people have in this regard?