Surely it's possible - likely even - that a small number of people will attempt to evade the system with forged credentials. That doesn't mean the whole system is a failure. If 99.99% are actually getting vaccinated, the .01% of fakers is going to be a very small health risk, especially if most people in the target country are also vaccinated.
Yellow fever vaccinations are just a piece of paper; anybody can fake one of those, but countries still have requirements in place because it's better from their perspective to have the overwhelming majority actually get vaccinated in order to travel there.
The situation with COVID is that most people want to get vaccinated, especially if they're going to travel. Vaccines are free and soon to be widely available in the US - why would I pay for a forged vaccine passport, when I could get the vaccine for free AND be protected against COVID?
Yes, access to vaccines is not evenly distributed right now, and I imagine that will be factored in when countries decide which other countries' vaccinated citizens to allow in.