Change it to a Aura, or Sphere (for XI players) effect.
Summary of how this worked in XI;
Some gear would have "Sphere: effect" as a stat, this would provide that effect to party members who were around the player with the gear (effectively like how Bard songs work).
So, if Morale worked like that, personally having high Morale would do nothing for you, instead it would boost your allies. This would add a new dynamic to PvP, where taking out the player with high Morale is not only possible, but an ideal goal.
Furthermore, Morale currently just boosts everything. Change that; my Morale on a Tank role should boost defense, my Morale on a DPS role should boost attack, my Morale on a Healer role should boost recovery, etc. That way it's a matter of "Who has the highest Morale? Which one is providing the most significant bonus?". Higher Morale would simply increase the effect of the bonus, but since a Tank is never going to get the defense bonus, they're not impossible to kill, rather than going for the Healer/DPS, the Tank could actually Tank, too.
If Morale worked like this, there would still be the advantage of getting Morale gear, but people without Morale gear wouldn't necessarily be left behind. If you end up in a party with no Morale what-so-ever, then you're obviously in trouble, but by removing (at least partly) the Morale bonus a role receives, it would be much more manageable to still put up a fight. You would simply have to play differently depending on your parties Morale and your enemies Morale. Such a onesided matching really shouldn't happen with the way PvP queues are worked, anyway.
I'm sure there are still issues with that, but I think it would still be an improvement, and could allow Morale to actually matter in Frontlines rather than just being a non-stat everywhere. All it requires is some serious thought and balancing (which I'm not paid to do). For Frontlines I'm also surprised they didn't take a page from XIs Campaign; let people buy some items which can boost their power in PvP. You could even have made those degrade based on your total Morale; zero Morale you get a huge boost to HP, capped Morale a small boost.
Overall though, something like this would create a new dynamic in PvP, which doesn't exclude players who haven't obtained gear. Tanks would actually Tank; they boost their parties defense, so you'll want to deal with them first. It would also put even more of an emphasis on splitting up your opponents, since that would also remove the buff.