One thing I will say is that when mixing, you don’t really want headphones with bass elevated, because that will result in a bass light mix, because you will be removing bass till it sounds balanced in those headphones with the bass lift. In your scenario, where people are listening on systems with a bass boost, this would result in way too much bass.
However, most mixers don’t mix entire songs in headphones, they will only use headphones for specific purposes, like for mixing vocals, or checking reverb tails etc, so they may chose a pair that is perfect for those specific areas.