Nope. This is the solution. And it's actually probably the best solution ...
If Nintendo put a headphone jack on the joy-cons, it would suck, because you'd be waving a cord around.
If Nintendo put a headphone jack in the Pro controller, everybody would complain because you would have to buy an $80 accessory in order to have voice chat.
If Nintendo required Bluetooth headphones, then people would complain because you would have to buy expensive air pod style things to voice chat. And also people would complain because you wouldn't be able to do local multiplayer with as many Switches, because the headset is hogging a Bluetooth slot.
And if Nintendo made voice chat a handheld only thing, people would complain, because then it wouldn't work while docked.
Also, there's Nintendo being worried about people (esp. kids) getting harassed. And they have a point: Splatoon is one of the few online shooters where I see a good mix of openly femme nicks in matches. Not being harassed for being a girl is a major perk of the franchise.
Pretty much everybody has a smartphone with a headphone jack, which makes it a nice way to provide voice chat for people who really want it. You're glancing at your phone to catch up on Facebook or look up super l33t strats between matches anyway, so it's not like it's going to add actual overhead to your life. And you can always invest in a pair of bluetooth headphones if you want to eliminate the cord.
Basically, sticking the voice chat on a phone does make a lot of sense, given what the Switch is, and what the bundled controllers are like. Not that will stop people from griping about it ... but they'd gripe about whatever solution Nintendo implemented, so I'm not sure the griping is going to bug the folks at Nintendo all that much.