are these meetings really so critical that you can’t miss them for a few times a year or even once a month?

No, nothing is critical, nobody will die when I'm not there. But those meetings are basically the core of my job, so it would be really weird to not prioritize them, they are the main reason why I'm getting payed.

I also do accommodate if I need to work outside of normal working hours, if I work with India or the US if the customer needs me earlier or later.

I guess that is why I kind of expect others who provide services also sometimes to go the extra mile, and to be honest most of the time you can find someone who does it.