As someone who occasionally reads but usually does their very best to avoid this topic due to its tendency to be a total minefield, I just wanted to let you know that this particular argument doesn't work for me at all.
You'd be better acknowledging the fairly obvious benefits that come from encoding so much more information into a single word, and then going on to argue why despite that it would be a good idea to move towards neutral suffixes.
When speaking Spanish, for example, I definitely feel the lack of information conveyed by su when compared to his/her.
It's not obvious to me that knowing everyone's gender at all times is important. In fact, as you say, there's a variety of languages where that isn't the case.
When I'm talking about someone I bumped into on the bus, why is it relevant what gender they are above pretty much anything else you could choose to encode there? I'd much prefer to encode, for example, my relationship with them - whether I'm close to them or not, whether I see them as equal, inferior or superior.
Gender is mostly a thing that becomes relevant when talking about relationships and sex or healthcare, and even then not always.
You'd be better acknowledging the fairly obvious benefits that come from encoding so much more information into a single word, and then going on to argue why despite that it would be a good idea to move towards neutral suffixes.
When speaking Spanish, for example, I definitely feel the lack of information conveyed by su when compared to his/her.