One thing I am missing: ID always shows me a list of streetnames(!) when adding addr:streets. And these streetnames are ordered in a way that most time the right streetname is the 1st or 2nd. But JOSM only shows me a list of any things which have a name, not only streets.
Since suggesting the contents of name=* for “addr:street”=* already is something special, I’d consider at least the second part (only using names from highway=*) possible. You could check here if someone already suggested that and, if not, add a ticket.