As long as special weapons, Exotics and abilities are allowed, Trials will never be a playlist where skill is the determining factor. It needs standardised loadouts and for ability usage to be restricted enough that the difference between classes is negligible. If the player count drops dramatically, then it's an admission by many that they can't play unless they have Hand Cannons and Shotguns, and refuse to use anything else; they would say it's because other weapons are unenjoyable, when it's actually because they're just bad at using them.
While stripping loadouts to the bare minimum might work, it would take away the feel of playing Destiny.
Kinda wondering, since the game mode is supposed to be a training ground, if limiting the effectiveness of insta-kills would be beneficial (shotgun, powered melee, etc kills). Like you get one quick kill but the next similar attempt won't kill without another shot.
Or, allow one-off kills only if you're the last team member alive, giving shotguns a Celerity like damage boost.