Sadly, it will also very likely be horribly over powered - and for that reason it should be reconsidered.
Some builds will definitely hit 200% DS during burst for a 50% increase in damage. Such a buff seems to be well outside the scope being for.
So I've been doing a deep dive on all the possible doublestrike stacking builds. Here's my rough conclusion so far
1) Every character can currently hit about 70 doublestrike from pastlives/gear alone. Combine this with 30% reaper boost and we have a baseline 100% doublestrike
2) Every pure class in the game has between 10% and 19% untyped doublestrike available. The exception being dragonlord and barbarian, which are conveniently the only 2 classes with access to +2 multiplier, so I think that's fair. Some specific multiclass builds such as swashbucking battle engineer warpriest can hit around 30% doublestrike, but I'm not sure this is a problem though given the dps loss in other areas for those builds.
3) All builds can get up to 21% doublestrike from destinies.
4) Combined, this allows virtually all melee builds to go from 100 capped doublestrike to somewhere between 130-150 depending on build, ie a 15-25% increase in total dps. I believe this is fairly balanced and reasonable.
5) There are only 3 exceptions to this: Vistani builds, 2 monk splash builds, and acrobat. Adding 30%/40%/45% doublestrike respectively. I believe this is where this buff goes too far. 30-40% additional doublestrike essentially makes one of these mandatory for all dps builds, massively limiting build options. Vistani is already the top melee dps, they definitely don't need an additional 15% dps above other builds.
6) The solution offered of adding more sources of moral bonus to doublestrike I believe is not ideal. For one, I think the total of nearly +50% dps is too much of a buff, and second, it will just be picking winners. ALL builds will need a source of moral doublestrike. Its just too powerful not to have. Its essentially trance 2.0. I think the better option would be to remove it entirely before it becomes this.