Why are they noticeably continuing this pillar?

My personal theory is that this is the closest sector they have to virtual reality (hey see it blossoming and being pursued by Sony, Google, and others). In toher words they see this as being the main arm in Virtual Reality. Not just the games but the divisions and departments that are already solidified within the sector from a company standpoint; all the software and hardware teams currently heading the division.

What do you think explains them still touting this pillar relevant in the face of the new Switch handheld? Just a cheaper handheld? 

It's because they need a profitable platform until the Switch has been out long enough to be profitable on its own. All things start of at zero.

People still need to buy the 3DS until Nintendo doesn't need them to anymore. That's why.

People who are asking this question should ask then why does Sony still support their old platforms with games years after the new one releases. It's because the platform is still selling decently!

It will have to be left behind which isn't unthinkable like the transition from GB to DS, that actually meant ditching a legendary brand but they wouldn't not admit it a first.

It will last until the end of the year until they milk it dry as a budget handheld with a big library, and they obviously have more titles that have been in development to release.

This is partially why the Switch is currently (and will probably be for some time) advertised as a home console first.

As long as 3DS game development does not interfere too much with the Switch's software output, it seems like 3DS+Switch is a relatively viable strategy (for the time being). Of course, the 3DS and the Switch will be competing with each other, a negative byproduct, but the Switch is close enough to a home console experience, and is being touted as such, to give it a distinct and seperate appeal to consumers.

The most likely resolution here is that Nintendo is going to stop developing 1st party titles for the 3DS after 2017 in order to focus on the Switch, but will not discontinue the 3DS platform ($$$).

Just in case the Switch suffered a weak launch.

Also consider many people bought a 3DS in the last year who wouldn't normally have figured it could be obsolete. We weren't 100% certain Switch was any way portable until late October. It's good to keep them engaged with the Nintendo platform rather than ignoring them.

Got to figure given the WiiU's state of decay - they also moved up Switch as soon as possible, causing overlap with existing 3ds projects.

I don't think so, just keeping the 3DS alive is a good buffer in case something goes wrong with the Switch

They already abandoned the Wii U and if they do so with the 3DS as well, it would be bad since Nintendo has invested a lot in the Switch

Keeping the 3DS going for awhile longer is a good idea for several reasons:

1. Demand for 3DS has never been higher. Thanks to the return of the Pokémon craze the thing sold out over the holidays and posted year over year growth. Nintendo would be stupid not to meet this demand.

2. With three separate SKUs that go for as cheap as $80, the 3DS appeals to an entire segment of consumers that just can't afford $300.

3. 3DS has smaller, more portable options than the Switch.

4. The 3DS has a large consumer base that is still buying games. Why not give them games?