Sick people receive vaccines for free or very cheap

Awesome, most vaccines last years or even decades, Covid is an outlier because it mutates so rapidly. But "sick people" makes zero sense, you usually get the vaccine before you get sick. That's the entire point (except for rabies, where you straight up die if you don't get the vaccine quick enough).

Sick people gets hope of survival to disease, hope which wasn’t previously available.

Also great, they get a chance, instead of lifelong suffering or death.

Sick people ask their governments to continue receiving vaccines.

Why would they be sick if they got the vaccine? Makes zero sense. The ones asking at this point would be the unvaccinated. Like a mom wanting to vaccinate her kids, so they don't get a crippling disease later in life.

People providing vacciones now are charging a lot more to said governments.

And then the poor countries simply won't buy them. Because they straight up can't afford them. There is a reason they aren't buying vaccines right now: No money. So if they try to charge a lot of money no one will buy and we'll end up with the current state (just with thousands more who are immune against the disease, which is still an upside).

Profit (which was the whole point, and not any “humanitarian” notions.)

You can't suck blood from a stone, there is no money, so no profit.

Every single vaccine dose that goes to poor countries is awesome. That's it. The alternative to getting the vaccine is to catch the disease unprepared and suffer lifelong complications (or straight up die). There is no upside to not delivering vaccines.

Are you confusing vaccines with medication? For example the Polio vaccine lasts for 10+ years, "sick people" are not repeat customers for vaccines. The only time you have repeat customers is when you are still applying the vaccine (for example Polio needs 5 doses, but then you're good).