I think this one has to be a case-by-case thing. Sometimes people who break up amicably and on reasonably good terms can go on to have a platonic, non-sexual friendship, and it doesn't feel complicated.
Other times, the nature of the breakup and/or the people involved can make an attempt at friendship a bit more difficult to do without resentment of some kind resurfacing, or even the opposite, love or sexual wishes resurfacing and comlicating things if they are both not on the same page. Sometimes it's best to make a clean break if the friendship isn't going forward in a healthy way or one of the two feel differently or harbors an agenda.
My ex-husband and I broke up very bitterly, but managed to eventually have some cautiously friendly contact along the lines of Christmas cards and maybe a couple of chit-chat/news catchup e-mails once in a while. But it never was a full friendship again.