While I do think it would further to the Servers role playing agenda I think it may also hurt the playing experiences of a few players.
For example if you play as cop for the majority of your time in Altis but have a crap few sessions there's the option to jump on as a civ and immediately have fun doing different things to your playtime as a cop.
However, If a separate bank account was brought in, it would mean that instead of this instance of jumping on as civ to have fun, people would jump onto civ and start making money....again. A lot of civ or rebel activities/pastimes are expensive and making the player have to go through the process of making money, despite having a few million in another bank, might throw some people off the idea of trying something 'different' in the server. Just my opinion, maybe there's a work around to the grind people would have to go through once more.