I completely agree that they shouldn't remove it. However, the issue is that the GamePad is something that most people just don't get until they get their hands on it. Anecdotal but many of my friends were sceptical about it, despite previously being Nintendo fans, and had no intention of getting the Wii U because of it. Then they tried it out for an hour and went out & bought a Wii U
I myself struggle to play games without it, even for just a map and inventory.
However, the first issue is a big issue. People just don't get it, so they don't see the value of it. Off TV play was the original intent of the Wii U, and it's great if you only have one/two TVs and you live with your significant other. Maps/Inventory are great, but as people will say, you can just press a button to load them (and take several seconds). People just don't see the point of it, and that's the issue that is putting a lot of people off, especially as it is such a focal point of the console.
As such, separating it from the main SKU and selling separately as a peripheral to IMPROVE the games is the only way Nintendo can attempt to get a bigger market with a lower cost console. If they just lopped $100 off the price now, and it took off, it'd do far more damage than the Wii U selling poor-to-moderate amounts (although still higher than the Vita...you don't see people seriously telling Sony to go third party/mobile)