Some math, which may or may not be interesting:
At 60 frames per second ...
* 16Hz is ~4 frames. That gives you a worst case of 8 frames of latency, due to tick, if two consoles push out updates with just the wrong timing.
* A 100ms ping adds 6 frames of latency. (Ping is round trip, so we don't have to add your ping to your opponent's ping; we'll assume that you both have roughly the same ping, or that the average of your pings is 100.)
* We might have another frame of latency due to buffering in the graphics pipeline.
* Our Lady of Google informs me that average human reaction time to a visual stimulus is 0.25 seconds, which is 15 frames.
So given a decent ping, a tick rate of 16Hz updates the game about as quickly as you can react to it -- 8 + 6 + 1 = 15 frames of latency in the hardware matching the 15 frames of latency in the wetware in your brain. You see a thing, and do a thing, and that's, in the worst case, when you see the next thing.
"Pro" players are going to have faster reflexes, and might be able to shave a few frames off of that timing. They probably also live on faster networks with lower ping, though, so the game isn't necessarily updating outside of their reaction window (and remember that the 8 frames of latency due to tick is out worst case scenario -- most of the time, the lag due to tick is going to be somewhere between 4 and 8. And each source of latency doesn't necessarily straightforwardly add to the others).
Basically, my back of the envelope math suggests that 16Hz is okay, for a tick rate, though it doesn't leave much room for latency in the network, video pipeline,or for lack of latency in the wetware of the squishy human playing the game. A higher tick rate is safer, leaving for more slop in the ping, and is friendlier to really fast humans. I imagine that the lower tick rate is part of the reason why the team at Nintendo went with regional matchmaking, mitigating some of the worst case scenarios with ping. I suppose time will tell whether the squishy humans feel that the tradeoffs that the dev team made, in terms of battery life, mobile data friendless, and kindness to the cpu in the machine hosting the match,were worthwhile. I know that I, with the reflexes of someone who is now pushing 40, am not the best judge for how this feels to a strapping young person in their 20s. But I don't think that the situation is quite as dire as you might think, reading through the rest of the thread.