Unlike Chris' suggestion they can't just ignore PvP, it is a big part of Destiny and there are a good chunk of players who almost solely play PvP. We were discussing this the other night and I apologise now as I can't remember the exact numbers but it is something like 60% of the community have ever tried a raid while only 20% have completed one. Obviously there are the strikes and NF's etc. but it gives some indication that, to a good chunk of the player base, PvE isn't that important.
I can't really comment on super charge time as I've not played enough control to know how it works in that. In the competitive mode, I don't see a problem with how slow the supers charge as arguably supers actually ruin the game mode as you either it is use your supers for an insta-win round or supers are used simply as counter to other supers. I can see (but haven't exeprienced so may be wrong) that in control with more kills and more points from capturing objectives that supers will build quicker.
I don't think it is clear cut as seperating PvP and PvE out to seperate mode and the game will instantly be better. It would still take careful balancing and arguable more balancing than currently due to effectively having 2 game modes. Bungie would also have to be careful not to run into the situation of there being PvP weapons and PvE weapons - a gun that is powerful in one should be powerful in the other. On balance though I do think they should seperate them out, we saw in D1 that in trying to balance PvP and PvE shotguns became OP to fuck then became uselss and Hand Cannons followed a similar path.