They also aren't "just saving 50 cents" by not including it because people aren't taking a number of factors aside from just the physical product itself into consideration.

Ultimately, it helps those who have their charger already while not actually negatively impacting those who want a charger as well (stores will be sure to point people in the direction of the charger).  It is a change in how a consumer is expected to pick up the product sure, but it isn't this malicious attack on the public that so many are making it out to be.  Is it going to be more profitable for them?  Absolutely.  Is it wrong of them to want more profits?  No.

Nintendo should start seling 3DS do-it yourself kits. You buy it it and put it all together yourself! They would save on manufacturing costs.

Honestly though, I wonder how people would react if the next iPhone came without a lightning adapter cable.

You meant 3rd-party charger probably. Anyways, I know, but it doesn't change much. It is annoying that it isn't included, but not the big deal. And I would get my fourth charger with the New 3DS ambassador edition I will get the next days.

There is a little bit of a price difference between the PS4 and XBoxOne power cables which have huge power packs included and a charger for a couple £ you can get from any game store.

That £20 is the price you have to pay from the official Nintendo store. I get that you can get them cheap, but personally I'd really prefer a 1st party one, don't really know why especially as I use any old usb cable to charge my phone...

My main point was that it has not been communicated clearly and can be confusing for first time buyers like myself

Not an equivalent comparison. It would be equivalent if the 3DS simply didn't come with a battery.  

If god forbid that 3rd party adapter causes an issue with your 3DS your warranty won't cover the repair charge. Although honestly I don't see how they would know.

Well the price point of the console itself would be £20 more expensive if they included the charger, so i dont see what you are moaning about?

They are doing it to give you options, rather than tying you in to having to get that specific charger. It gives you the option to save a little bit of dolla

Have been using 3rd party chargers on all my DS's for years and never had a single problem. Nothing would happen.

You are cluching at straws to keep hating them for this 

My comparison was more aimed towards Nintendo, not the XBox One, since PS4s cable being excluded can carry a similar excuse to what Nintendo is giving., although Sony would be a bit easier to swallow since figure-8 power cords are not propietary and actually quite common.