That's absolutely a good thing. But you'd be a moron if you thought that we could have "vaccination passports", for example. That somehow since you've had the vaccine, you could go back to shaking hands, singing loudly in church choirs, restaurants could open to 100% capacity, and music events can return in bars. It doesn't. Because if anybody near any of those scenarios is not vaccinated, or they end up in that 5% where it isn't working for them, you still are contributing to community spread. And the more people who show symptoms with community spread, the more your ICU beds will fill up.
The good news is that it should reduce those incidents, definitely. But human behavior is a weird thing. Volvo drivers are notorious for taking aggressive risks because they have faith in the safety of their vehicles, ultimately making roads less safe - not more. (See:
Risk Homeostasis Theory.) Thus it could be quite likely that vaccinated people could participate in extremely risky behavior, creating havoc for everyone around them who either lacks immunity or isn't vaccinated.
Which makes me think of the dangers of driving in D.C. in the snow, where you have a mix of transplants in the North who know how to drive in the snow combined with transplants from the South who think they can emulate them... causing massive car wrecks.
Your assumptions about vaccine distribution here are also pretty unrealistic... it's a mass scale and not everyone will be able to get it at the same time. Not everyone will react with the same efficacy (think: all the obese people in America where flu shot efficacy is often poor). Not everyone will be able to take it even if they have access (allergies, immune system compromises, anti-vaxx nutjobs, etc.). And there will be people hopping on airplanes and flying to nations who are wholly unprepared for carriers with zero social distancing instincts.