My advice is slightly different from the above. I think that how you'd want to manage this depends on the variety of each tree. For example, English Brown Turkey makes brebas that taste great, in fact I like them better than the main crop. Furthermore, the English Brown Turkey main crop figs take so long to produce and ripen, that in a short growing season it's unlikely that you'd get any main crop figs successfully ripened... the season here in zone 5 is just too short (and probably down around NYC too... some of the NJ folks have told me they never get main crop EBT there... I think it was Vasile who reported that but not sure). Luckily though, English Brown Turkey makes lots of brebas here. So for English Brown Turkey, I'd suggest that in your area, leave all of the brebas on (because you're unlikely to get any ripe main crop from that variety).
That principle generalizes. For varieties that require a long season (longer than you've got in Queens NY) to reliably produce ripe main crop figs, then I'd suggest leave all the brebas on those varieties of tree.
I also don't know to what extent the ripening of brebas really "takes anything away" from the main crop. Maybe some of the experts on here will comment about that principle. But for a healthy mature tree, leaving the brebas on to ripen might not have much impact or reduction of main crop production. Aside from the maturity and size of the tree, there are probably other variables to consider too. For example, some varieties may have main crops that are less affected (by breba ripening) than others. (So this factor also might be dependent on the variety).
The net of my point is that I think the answer to your question is variety-dependent. And for one specific example, if you've got English Brown Turkey around the NYC area, I'd say leave all the brebas on.
Mike central NY state, zone 5
<edit: 32 minutes later> P.S. I usually just leave all the breba on my trees. Lots of them fall off on their own. But I like letting the tree choose what fruits to ripen, rather than me knocking off breba in the hopes of getting more main crop. The one exception I practice is when the trees are very small and/or young. When they're small trees, especially first-year trees that were just rooted (but sometimes smaller second-year trees too), then I knock off most figs those trees produce (when the figs are small). (For me, this applies to any figlet on a too small/young tree, whether breba or main crop). That's because I want the tree to put its energy into getting top growth and root growth, not into fruit production. But after the tree has reasonable size, then I stop knocking them off. (And there are probably some differing opinions about what constitutes "reasonable size"). I don't really know if that's any accepted/recommended practice, but it's what I do.