That is ever the fun discussion and someone will probably have to probe something to provide a satisfactory answer.
There are several competing factors in this.
i) Deep discharge. Rechargeable batteries are not all that much different to the bit of zinc, copper and lemon/potato back in school, just that they use a so called half reaction that you can undo easily enough. By drawing too much power (and it will waste power sitting in a drawer, albeit less than what it sounds like the Wii U quiescent current, current you lose sitting in a nominally unpowered state, is) and the half reaction becomes a full reaction which is hard to recover from and never likely to get back to 100% even if you do manage it (which is tricky without quite serious gear that not all devices have as that costs extra to do and theoretically it might never get there/you can sell a new battery/repair service if it does).
ii) Full charge and batteries. So much myth, rules of thumb, misinformation, irrelevant information to modern chemistries and more in this one. You don't just take a 3V rechargeable battery, apply 3V from the wall to it until it is full and move on from there. You have to baby things along a lot of the time, slow sections of certain voltages, certain current (see constant current), limits on currents (fast charge does kill batteries quicker, though it is fast to charge) and more boring stuff you can read about on a battery datasheet or charge controller article somewhere.
Anyway most chemistries will split into three broad areas. Deep discharge which we already covered, normal charge and top up charge. Normal charge is why things go from 20% to maybe 80% in a short time but the last 20% takes an age as that is in the top up range. Top up is also when a bit more damage can happen and things get a bit excited hence why some suggest to store things at 80% or whatever rather than full, albeit that means you charge more often if you are leaving it (the memory effect some older chemistries had is not a thing for lithium). I read conflicting reports on practical tests for what goes with lithium on this one. Storing/keeping between 50% and 80% is probably going to be the safest and if you do decide to play it a few times during that period then doing full charge cycles in general is going to have more of a deleterious effect.
What the Wii U will do on standby is then anybody's guess, though I would predict it goes for full at all points in time or maybe goes for full and then kicks back in when it drops below top up -- Nintendo can sell you a new battery and stops their power hungry tablet display from getting a rep for low battery life.
You also have the notion that you are wasting power by leaving it on the whole time and that can add up to something reasonable, especially if power prices are as much as they are right now and we are measuring in years. It will pale in comparison to leaving an electric fire/electric shower/air conditioner/electric oven... on for a few less minutes over the course of a month or two but hey, and if you add that up for monitors, TVs, computers, random gadgets and more then yeah.
Also say totally disconnected in a discussion like this and people will tend to assume you opened it up and unplugged/snipped a wire as opposed to unpowered and whatever its idle/rest state is.
Finally we are just starting to see custom batteries become a thing to replace old devices with random connectors/sizes so you might even get away with not worrying so much if it does not work in 10 years and you then face what people do today where old official stuff in 99% of cases will be deep discharged owing to sitting in a cold shed for 15 years, salvaging from a previously working device is tricky (also likely to be well used), hoping something is cross compatible or buying something probably dodgy from the far east or going more custom still and converting it to another form factor that is more common. There is a possibility, albeit small, that said replacement in 10 years bumps it from the mild afternoon session and up into the up into higher runtimes as well and you get called the 2035 equivalent of a hipster for sticking with the old battery chemistry.
