I would say I fall somewhere in between. I don't really mind it, but it can get to be a bit overwhelming in the garden. And even then I sometimes leave it to act as a living mulch. This year I've given in and am using the farmers recommended plastic mulch. Incredibly strong winds and heavy rains can quickly erode valuable topsoil here, not to mention the somewhat long hot, dry spells that come as the spring turns into summer.
Purslane doesn't ask for much - hence, it's now naturalized state - so it isn't using valuable nutrients that other garden crops might need. The seeds are viable in the soil for about five years, so it's also bound to rebound even after a heavy harvest. It's so ridiculously good for you and tasty that it seems like a no-brainer to eat it. (Not to mention I didn't have to do anything to encourage it's growth.) If I feel it's getting a bit out of control I harvest a big bundle and take it home to add - stems and all - to salad. One grower made what sounds like a fantastic stew from a good round of weeding.