No, you're just assuming that, as most pro-vaxxers only conceive of people who don't get vaccinated as being "anti" vaccination. One can believe in the effectiveness and safety of vaccination and choose not to get vaccinated. But most pro-vaxxers see everything as black and white as the people who think vaccinating doesn't work or isn't safe. That's why the best response in this thread was the first one from the guy who pointed out that people love choosing sides and fighting 'others'. Everything in your reasoning is based on the demonization of people who don't get vaccinated, attributing every problem stemming from this pandemic to them rather than to the virus itself. This type of attitude and view are encouraged by the media and companies which is why people who don't want to get vaccinated get so loud in their protest. Then pro-vaxxers cherry pick the dumbest of those voices to argue against them to further consolidate their sense that they are right about everything they already believed. Toxic cycle.
Vaccination is an option, not a necessity. And a mandate or strong pressure to force the entire population to vaccinate is not at all based on reason or science but rather greed and lust for power. People who love to invoke science in this debate are often the ones who show the least nuance in their thinking even though science requires such nuance.