it really is baffling why there is no voice chat
It takes up bandwidth[1] and the actual trend data is that public non-party voice chat usage is
dropping. A large amount of users are either in system chat (Xbox/PS) or using Skype or Mumble/Ventrilo to talk to their friends.
Add the E rating, which causes a lot of developers to outright drop online functionality completely (Every mainline Rock Band supported online play, while Lego Rock Band didn't even have it, because it was the E rated one).
And I'm not even defending Nintendo here. More and more AAA games on Xbox and PS are starting to exclude public voice chat. Halo Reach greatly cut down on who you could hear. Halo 4 outright does not let you hear anyone outside of your team. Destiny launched with no public voice chat - they later added an option to publically voice chat, and I've yet to hear a single person actually use it on PS4.
My guess is Nintendo may be working on OS-level voice chat anyway, so there's no reason to implement it in Splatoon because the statistics show that party chat is the dominating method of communication on the other two consoles. This isn't the days of Halo 2 anymore, social chat is fucking dead.
1. This was the reason why the voice codec in 360 games got better over time, especially in the Halo titles - Microsoft determined a bandwidth limit for games, so you had to choose a codec and quality setting that wouldn't consume the bandwidth. They slowly bumped up the limit and the voice codec was nudged up along with it. Voice chat is not free, bandwidth wise, and many developers now prefer to design their networking with the assumption people are in party chat anyway and use more bandwidth for game data comms than voice comms.