Unlike most people ITT, I'm of the opinion that the second screen needs to go.
Personally, I like HUDs. I think they give games a uniquely pleasing kind of aesthetics. Stats, life, score, level etc. stuff fits better on the screen where the stuff is happening for me. As such, I prefer multiplatform games on a single screen.
I believe that whatever novelty the second screen had was explored during the DS era. The World Ends With You and 999 are some stellar examples. I find no such example for 3DS except the whole "map" ordeal. 3DS' touchscreen being a low-res, resistive glass hot piece of shit that was smaller than the main screen pretty much relegated it to being an "info hub" for most games. As I stated before, this takes away from my enjoyment since it simplifies the main screen's HUD. Moreover, it's more of a hassle to keep looking at the lower screen to get info and use power-ups and stuff at times (a la New Super Mario Bros or SMB 3D Land).
Don't like the clamshell design much either, loved it on the GBA SP but with two screens it just looks incredibly ugly. Didn't like it at all on DS or 3DS, and since a touchscreen is practically impossible with GBA SP's design (above half screen, lower half controls) I'd much rather a run of the mill, horizontally held device (or vertically or flippable, basically no hinge). As for keeping it covered, just get a case. Not as portable, true, but safer to carry IMO. Moreover, it means we can finally get a proper analog stick on a Nintendo handheld.
Unless the only format we get is some 3DS XL sized giant, the dual screen also limits the usability of both screens because their size keeps games with detailed graphics getting ported to them since they'd look too crowded on those small screens.
There's also the fact that with the amount of power Nintendo puts into its handhelds, a single screen would be able to display much better graphics than two atrocious screens.
In order to make third party games look like they do on other platforms and possibly get rid of the HUD and inconvenient porting issues, I'd say it's for the best if dual screens go.
The 3DS' graphics are ATROCIOUS, without 3D on pretty much the only visually pleasing 3DS game I've seen is A Link Between Worlds and maybe Ace Attorney Trilogy. If Nintendo doesn't port over the 3D and also makes the platform's games look like painful, atrociously low quality, graphical messes then I'll be very disappointed.
I hate playing non-innovative (a la TWEWY) games on the touch screen, they KILL the immersion thanks to the dual screen setup.
I detest the second screen. I hope it's gotten rid of.
edit:
An attachable second screen would be a wonderful idea, (3)DS BC + stops the "MY MAPS" crowd.