An idea of what Nintendo's new subscription service that's replacing Club Nintendo might be.

[SuperNova]

I'm not quite through yet, but so far, all I'm thinking is: Why would Nintendo do that?
If their vc games didn't sell at the prices they are asking they would lower the price. Obviously people are willing to (begrudgingly) pay up.
You delivered the math yourself, if Nintendo can get 20$ from their customers, they wont ask ten and give them access to even more content than they would have previously gotten with 20$.
That's just lost money for Nintendo.
The trick of a successful subcribtion service is to look like you give good value while actually not giving that good of a value after all. For example, by limiting the available games every month, so that people keep up the subscription in the hopes that the games they want will come into the rotation, or by exploiting casual subscribers that pay the relatively low price every month but don't use the perks all that often.

I think delivering that service on smart devices at a reduced cost actually does the opposite of what you're anticipating.
Instead of roping in new customers, the loyal consumer base gets screwed over in pricing as a reward for buying the console, while the smartphone crowds have absolutely no incentive to buy the console. After all they're getting hundreds of Nintendo games at a cheaper price than they would on console. On top of that they are a casual audience so they won't care for better graphics or the newest iteration of a game. These people play flappybird, you're not going to woo them into buying a console by giving them free games on a device they already have.

A better way to do that, is to offer a (relatively) more expensive/more limited version of the service on smartphones (while still offering an acceptable pricepoint) and having the service be cheaper/same price +offer more perks on the console and maybe implement something like cross play that allows console owners to access the smartphone service for free, with crosssaves etc.
Whatever you do, the console has to look very attractive from a casual consumers perspective, much better than their current smartphone deal.
(Aside from all that, I don't think nintendo will offer vc on smartdevices at all, as they've previously mentioned they won't do ports.)

On top of all that you propose 25% off new releases and free games+merch through a club nintendo like program....again where are the perks for Nintendo?
The idea of a subscription from the companys side of things is that you give a custumer small to middle sized perks in exchange for a guaranteed monthy fee. What you're proposing is more akin to an ongoing nintendo clearance sale.

Now, I don't disagree completely, I think a vc subscription service could work, just not the exact way you're proposing it, certainly not with the insane perks smartphone gamers would get with your plan. I think nintendo would bleed money compared to now if they did it exactly like you're proposing, since it has insane overall value and would be every fans wet dream of a subscribtion. Too good to be true.
I could see a service for vc where they limit your access to the games either by having a weekly/monthly rotation for you to choose from ala ps+ or give you access too their complete library but for a limited amout of time per game. If you want to keep playing you have to renew the sub.

After reading the rest, I realize option 2 (time limitation) is pretty much what you're proposing. I'm still not sure I agree with the way you'd want to it but it sounds more reasonable now.