I don't know if willingness necessarily implies conversion. Many willing people probably don't become vegan because of peer pressure, spousal or family pressure, or just the fear of "seeming different." At a work meeting a few years ago, I ordered a "vegan breakfast." The admin called out the orders and, when he arrived at mine, he gave me a look I'll never forget and barked at me "are you VEGAN?!!?" in a very unkind, mocking manner. All in front of numerous co-workers and managers. Other people see that and don't want to submit themselves to the same treatment. In some circles, being vegan still carries a significant stigma. I know, I've experienced it more than once.
I would also be careful with utilitarian ethics. It can be used to justify lots of nasty things, such as "10% of the population enslaved for the greater good of the other 90%." "Greater good for the greater number" can turn into a slippery slope pretty quickly. There are better ways to justify veganism, such as the dimunition of suffering. But I do agree that the world would be better if everyone were vegan, so don't get me wrong on that. I'm on the vegan side, but I think making everyone vegan is a very complicated question. Plus, again, it's only hypothetical. I'm just sharing my thoughts, I'm not trying to be difficult.