I still don't buy what everyone seems to always claim - that people thought it was a $350 controller instead of a new system. I mean maybe some of the Wii audience thought that, the type of people who had never bought a video game system other than a Wii, but anyone who remotely is interested in video games knew that it was the successor system to the Wii. So not understanding that it was a new system is definitely not what let to its horrible sales.
As someone who has owned every Nintendo console other than the Wii U, I can tell you why:
1. Asymmetric gameplay seemed way more awkward than it was interesting.
By making the system have one big massive unique controller, and then everyone else had to have Wii controllers, it seemed like Nintendo wanted it to be primarily a one player system, but oh by the way if you happen to have Wii controllers laying around other people can be like secondary players. It felt like one of those games where one person gets to do most of the play but they tack on a second player who can technically play but barely does anything (I think Mario Galaxy had that, where player 2 could just control the cursor to pick up the little star bits or whatever) but applied to an entire system! Really just an awful idea.
I know Nintendo wanted people to think it was this unique experience and then for the 100 million users who have a Wii you get the benefit of not needing to buy extra controllers like you normally need to with a new system, but instead it came off as a single player system with a big awkward controller where everyone else in multiplayer were second class players.
2. This awkward one-player focused experience costs $100 more than the super fun Wii experience cost. And it was clear the extra cost was due the big awkward single-player controller. So Nintendo was charging a premium for something uninteresting and awkward.
3. No killer app.
Wii sold 100 million because everyone was playing Wii Sports and having a blast and if you didn't have a Wii everyone was like uhh why are you still playing with boring regular controllers, you gotta get a Wii! If you go to someone's house and they had a Wii it was like omg let's play some Wii! And then of course it backed up Wii Sports with a bunch of other fun casual games, as well as some great traditional experience games. Switch launched on the back of the revolutionary BotW, had a great Mario Kart just after launch which while not new was new to most people, followed it up with Mario Odyssey, and plenty more smash hits in the years to come. While both of those systems had main features (motion control, play anywhere) that enticed people, they launched with games everyone had to have and had lots of other great experiences. Wii U...while it no doubt had some good games, can't really think of a single game that stands out or comes off as a system seller.
Nintendo pretty much needs to launch with an amazing Zelda or Mario game, or it needs to have some other unique game at launch that everyone wants to play. Not launching with a fantastic mainline Mario or Zelda game is a guaranteed huge blunder for Nintendo. SNES launched with Super Mario World. N64 launched with Super Mario 64 (but because third parties entirely left Nintendo it barely had any games coming out which is what caused it to have low sales). Gamecube, what do you know, no big impressive must have Mario/Zelda launch game (though Rogue Squadron 2 was incredible) and the system sold really poorly. Wii had Wii Sports and also Twilight Princess but it sold primarily because of word of mouth about Wii Sports. Switch launched with BotW. Switch 2 will no doubt launch with the next 3D Mario game. Looks like the Wii U had a lot of launch games but there was no killer game. Heck it launched with a 2D Mario, and worse, it was the third NSMB game, so it wasn't even a new experience. And from playing that game on Switch, its a pretty mediocre Mario game too. 2D Mario is very popular, but the series is not worthy of a must have launch game and hasn't been since the SNES. You don't buy a brand new system because of a 2D game, especially not one that doesn't even feel new.
Wii U should have launched with Mario 3D World, but even that wouldn't have been enough. It's an incredible game, one of my favorite Mario games, but for years until I finally played it I thought it was just Nintendo being lazy and not wanting to make a full 3D Mario so they went with a 3D Mario game in 2D Mario style gameplay. It wasn't until I bought it just to try it out that I realized how wrong I was. That is not the sort of game that sells systems. And then Wii U didn't even have a Zelda game until the Switch launched, and that game was the killer app for the Switch.
So Wii U had no big Mario/Zelda or unique must have launch game, no system selling Mario game at any point, and no system selling Zelda game until it became the Switch's system seller.
4. The 'hook' of the Wii U - that you could play on the game pad screen when other people were using the TV - only works for people with a busy TV household. This is a complete non-feature for any single person, or for any family that has a separate video game TV and main TV (for example, growing up we had the TV with the video games in the basement, while the main TV was in the family room). So in tons of homes the idea of being able to keep gaming while someone else was using the TV isn't even a problem. That seemed to be the big problem that Nintendo was trying to solve with the Wii U, but it wasn't a problem for probably most people.
Summary:
System was doubly designed around two features that were either awkward or was a solution to a problem that isn't a big problem - awkward one-player focused asymmetric controller setup that nobody wanted, and playing while someone else is using the TV. And you had to pay $100 extra for these two unwanted features compared to Nintendo's previous system. No killer 3D Mario/Zelda launch game. No killer must have game in general.