Are you talking about cutting all the way throughout the slab? Why? Does that joint go all the way through now? Or is it just a stress-crack-hider (sorry, forgot what those are called).
Using the existing expansion joint might save a little work. If he does that, why bother with the planter? Just widen the joint enough for a 3/4" pipe, or that existing hose. Just run it from the slide, over to the joint, along the joint, off the slab, then over to the pipe (or move the pipe over to the end of the joint). The reducer can be there. He doesn't have to run 2" pipe anywhere else. Less cutting. Looks to be less than a foot between the end of the joint and the slide. Doesn't look to be a foot path. Done.
Sure, it'd look better if it was all hidden, and it that's what the OP is after, go for it. No one but him is going to notice if that hose comes out of the concrete right under the slide, at the end of a Sikaflex-filled trench, or via a buried pipe, or a foot over by the end of the existing, widened expansion joint, or out of the side of the planter. He should do what looks right to him, but he'll be the only one it matters to...
Really comes down to how much effort/time he wants to put into it...