It all depends in the example. Magic effects can definitely get a little oomph from it, in battle or on the overmap animations. Maybe someone casts Volcanon, and an eruption of molt spews out towards the player? In terms of aesthetics, gale-thrown leaves can also swish in and out of various levels of depths, both behind characters and in front of them (close enough that the depth appears to jump out at you at times). Warping used to caste pentagrams on the floor--one side of the symbol can stretch around a unit, extending "out" of the screen at the point nearest to the player.
I don't agree, to put it bluntly. I don't notice little touches in games and think "they're cool but if they were in 3d they'd be so much cooler". For example, in Metroid Prime 1, when using the X Ray Visor, you can see the bones in Samus' hand, and they correspond to the symbol for each Beam. I can't say that would really be improved by the addition of 3D.
I shouldn't think you'd agree a static effect would benefit from depth perception. They're static--it is the animate that makes better use of it.
Sadly, we've already seen the POV for commanding units, so not many effects are likely to make it that far up, and in battle, we have to deal with the camera angle that (recently) became less stoic and more dynamic. But there's still room for interesting effects to pop in and dazzle the player here and there.