There are two advantages and two disadvantage of capacitive (=multi-touch) touchscreens:
+ They can detect multiple fingers at the same time of course
+ They require less pressure to detect touches
- You cannot use styluses with fine tips on them

Multi-touch touchscreens are a little more expensive as well, but that's not the reason Nintendo chose the seemingly outdated resistive one:
- A multi-touch capable screen would have ruined backward compatibilty, as many of the old NDS games are unplayable with fingers/without a fine tip stylus. Think of painting games like the very popular Art Academy or a game like Picross for example. Such games simply require the possibility that the user can target very precisely
- 3DS-only games could partly solve this problem by using user inferfaces specially designed for capacitive touchscreens, but certain types of games (like the paining games mentioned before) would be a general problem
- Multi-touch on such small screens has few practical advantages, especially if a device has analogue and digital buttons for gaming anyway. Using one finger on my NDS for example is already enough to obscure huge parts of the screen. Use two fingers and you'd probably hardly see anything.
- Using fingers might also ruin the 3D effect (not sure about this one though).

To sum it up, the 3DS solution makes perfect sense, people would actually be complaining much more if 3DS had a multi-touch capable screen. For gaming, multi-touch has few real advantages anyway. The only thing I'm ever using multi-touch for is pinch-to-zoom and I would personally prefer still being able to use a stylus for fine aiming. These styluses/pens for multi-touch displays are a compromise at best.

Yeah well, what happens when you lose your fingers?

I usually use finger/thumb, i.e. OOT inventory, no problem with that.

Stylus is when I need accuracy for games like Picross.

I've owned devices with resistive screens like the DS or a WM phone, and I've always used my fingers whenever I can, only taking out the stylus whenever precision was needed. For example my daily use with the WM is sans stylus, just like you would use a capacitive screen, but instead of using my finger tips I use the side nail of my thumb and it works great. Sure I have to apply more pressure than what I do with my iPod touch, but it works good enough. Moving to games, the DS is great. You have the option for finger or stylus with the system. When a game requires dexterity and precision, you slide out the stylus - if it's just menu's, etc, the finger is enough. And multi-touch? Resistive screens are able to detect two points: http://gamrconnect.vgchartz.com/thread.php?id=6592

PS: PPL use protective screens. I use them in all the gadgets that I use a lot, be it resistive or capacitive.

I get it, that it's not cool unless Sony makes one.