Just because sales aren't double in number doesn't mean people aren't wanting to buy it at regular price. 
Those segments are consumed over time.

PS4 was bound to get to a lower price point. It did come out in 2013. But even at 400 or 349 it sold very, very well.
Of course that the Slim model is selling better than the PRO. The PRO has no real value besides visual diferences. And even then, you have to have a 4K TV.

The question is if Nintendo is selling the Lite console to the same people who would buy it a bigger price anyway. I, personally, believe so, as the demand for the original and it's appeal is still there.
To me it feels like leaving money on the table.

Yes, they do lose money from the software, but not by much.
And for people with low income, that's probably more appealing to the eye - as in, more value at once.

I've seen Lite versions of smarthphones, compared to the premium versions, cost way way less.

The BC micro was a later ireration.
The DSi had indeed a worse battery life, but the lost of BC on that device and the others you mentioned was not relevant.

Losing a selling point like the 3D screen was for 3DS or inability to fully "switch" between game modes, is relevant. Specially on Switch's case, where it stops being everything to just a handheld - or if had become a home console only, my reaction would have been the same.

So, my point still stands: this transition, of this magnitude, is, to me, a bad move.
If they wanted to do it later in the lifecycle, so be it. But now, where "Switch" is still being sold as a whole?
Also, the other flaws in newer models, that you mentioned, never were recipe for confusion nor did they take away from the main experience, ddi they? In this case, that's what's happening.

I never said that going after price concious people was a bad move. I just think there's a right time for that. And that time, for Switch, isn't now.
The way i see it, Nintendo will be selling a cheaper console to people who would buy it for full price.

You lower the price for late adopters, not now. And you also add system sellers to the mix at lower price points, too.
But that's just me.

That's not what i'm trying to say, at all.

Yeah, in Japan, it makes more sense for a handheld only device at 200$.
But why is Switch still behind 3DS? Is it just a temporary thing or not, like 3DS was once ahead of DS? Is it because of the lack of proper support instead of ports and more ports and remasters?

When you go after price conscious people so soon, you are leaving money on the table. Because a chunk of that market who would buy it at a higher price, will now buy it at a lower price.
Second, this isn't just a cheaper version with smaller alterations. This is a console called Switch Lite that can no longer switch. And that's big! It's big because the messaging won't be clear (no two type of commercials, for exemple) and it's big because people were sold on the ability to switch (hence the name) and that won't happen anymore.
Question is: will people care or not for the change? Given the appeal and all the propaganda, i think it's safe to assume they will care.