No, I don't think it's a reasonable request. The best way to forestall speculation is to just say what happened. Presumably his family already knows so it's not going to shock them.
Or only some of his family know, and it may be best that for those that haven't heard yet the best people to tell them would be the other family members that do know.
THIS IS BAD FOR EVERYONE!
Yes, it's embarrassing for the family (though it shouldn't be) because they feel like they can do more.
But, it the prevalence needs to made public so we treat these things like the crisis they are!
And worse, in this case, people are even drawing ties to the vaccine!?!? What an insane intellectual lottery to play. But that speculation WILL cause direct negative outcomes!
Ugh, just ranting b/c as mentioned I have first hand experience with "it wasn't alcohol/drugs/suicide, it was cardiac arrest."
/End rant
Your reply talks about other families who lie and state a false cause of death, which would be morally wrong but in this case is completely irrelevant because that's not what's happened.
The one bit of your comment which is relevant, I think, is wrong: namely "the prevalence needs to made public so we treat these things like the crisis they are". We have anonymised statistics on suicide and overdose deaths. That is not the same as demanding a specific person's cause of death - and the sense of generalised academic interest you're alluding to is plainly not the reason for which people are curious about how he died. I wish we would get a grip on ourselves here, because it must be upsetting for anyone who knew him and is reading these comments, as surely some of those people are.
Edit: I died of a heroin overdose, briefly, before I was resuscitated. If I'd died permanently, my family may well have wanted to keep that information off the record permanently (easier in my case of course because I'm not a public figure). It's easy to think in the age of Wikipedia that all information is in the public domain and belongs to everyone. It's not, and it doesn't.
That's a bit of an assumption. Working out how someone died can be tricky.