Burst largely isn't a problem. Stampede is broken, stacked warrior CDs are too good if you can't avoid them, and deep freeze is still pretty scary. Aside from that, it's possible to keep yourself alive through a 20 second chain of instant CCs on your healer. Far from broken burst.
You also can't get rid of PvP stats because you disagree with their tuning. The whole point of PvP power, resilience, and baseline resilience is that they can drastically scale any factor in PvP without it affecting the rest of the game. If burst was too high across the board, resilience would get a buff. They could also nerf PvP power, but then real stats might come out better and I don't think they want that.
The "ilvl squish" was a proposed solution to large item level jumps between expansions. It has nothing to do with the gap between two ilvl tiers (which hasn't changed, btw). Furthermore, the difference between ungeared and geared players is much much smaller than in the past due to baseline resilience. Any gear difference will always be a huge disadvantage in PvP--that's just the nature of it--but an ungeared player can put up a better fight than ever before.
Healers don't need a nerf either, or at least not to their throughput. Since you didn't specify, I'm assuming that's what you're talking about. What should probably drop is mana regen. As crappy as it feels to win just from ooming the other team's healer, games can be so long that I'd rather that be the case. Removing drinking would be a good start (or maybe enough). It doesn't show skill or poor strategy when you can drink; it's just the nature of the game that you'll be able to do it now.