The DS line was available at retail from 2004 to 2013. GBA lasted around 9 years too. The 3DS is two years short of that right now.
Something the 3DS has that the GBA/DS didn't have is mass digital availability for nearly every game, so even if they slowed down or even stopped production of some of the older titles, they are still available for purchase digitally at any time.
With the GBA and DS, it was a bit hard to find some of the earlier titles and you'd often have to rely on the secondhand market.
Maybe they could stop producing new games at some point (and I guess that is the point being put forward here), but at the very least I'd not be surprised if the 3DS remained available for much longer than the GBA/DS were.
Also, I guess the Switch would be the first Nintendo handheld to have no backwards compatibility whatsoever, so that adds another incentive to keep the 3DS supported (keeps DSiWare and 3DS titles available and playable.)
Consider that a parent with two children would have to pay $600 for both of their kids to have their own "handheld" (Switch), while
two 2DSes only sets them back $120-$160. Even the N2DS XL brand new retails at only $150, which is half as much as the Switch while still having tons of amazing games. It's well worth continuing the support for it.
Don't forget that $250 was too steep of a price for a handheld (the 3DS) and they had to cut the price by $80 just a few months after release. $300 works for the Switch because it is ultimately a home console, and this is what the average buyer is buying it for. It just happens to also be playable as a handheld, which makes it even more attractive.