All good points.
Fresh herb rubs--those made exclusively with fresh ingredients--can remain or become pasty when used for low/slow cooks, especially when you figure in the rest period. I really like fresh herb paste rubs for shorter, high heat grill-roasts though and make them more often than not for those kind of cooks.
For low/slow cooks where pastes are typically used--like with jerk pork or conchinita pibil, e.g--you can wipe off most of the paste after marinating and before cooking; you can wipe off all, some, none, or just a little after cooking and after the rest, working the remainder into the meat as you pull or chop it; or, after marinating but before cooking you can wipe off most of the marinade and apply a dry rub using dry versions of key elements of the marinade.
For low/slow cooks with 'typical' dry rubs you can use fresh herbs without a problem since the bulk of the rub is dry ingredients. For best results, imo, mince the herb(s) very finely.