Then why did they use the port? I'm guessing it's the obvious answer of "it was cheaper".
As much as it pains me to say it, a "pay us to use the port shape" group like HDMI that will threaten litigation unless you pay them to use the port would probably have prevented this kind of thing from being as widespread with USB-C as it is. While just about everyone doesn't want that to be the case (myself included), I don't see any other way of aligning incentives to make it harder to use the port/spec incorrectly than it is to make it correctly.
More that cheap it was convenient: You solve the whole power, video output and external devices problem with a single chip on both side. And it also look nice compared to any usual docking port.
It solved enough design issues for them to let go their old habit of having proprietary connectors for charging. Which made them a lot of money.
For what it's worth, the linked article I think is misleading as to how incompatible the device is. I charge my Switch regularly at work with a Lenovo 45W USB-C power adapter (model: adlx45uccu2a), it seems to perhaps take longer to charge than the Nintendo one but has worked reliably. Unfortunately I have tried several 3rd-party USB-C HDMI adapters with no success, though there are several options for HDMI+power on Amazon that reportedly work -- as I understand this is simply because the Switch does not enable video output unless it is also on AC power, so you need a combo adapter.
I've also charged my Switch with a random USB-C cable that someone let me borrow. It's a bummer that it doesn't handle HDMI properly or whatever else people might want from it, but being able to borrow a commonly-used cable and charge my Nintendo device (or any other dedicated gaming system)? I don't know if that's ever been done before... I certainly haven't owned one. And it's a nice step forward.
Fun fact: the Switch does output a flavor of DisplayPort to the dock, which converts it to HDMI using a Megachips STDP2550 MyDP-HDMI converter for output to TVs[0]
No, you can't. You can convert DP to HDMI, not the other way around. DisplayPort uses packet protocol for its data (so it's almost network data like), while HDMI is just using digital signal. So it makes sense to always prefer DP.
Make popular and cheaply available ($1 - $3) a simple device that can plug into a port and pound the device through all the modes, blowing it up in spectacular fashion if it's not compliant. Make them ubiquitous enough that mischievous sorts are prone to quickly destroy any device put on the market with flawed ports.
Note: There is probably an ethical issue with this, but it doesn't jump out at me.
As much as it pains me to say it, a "pay us to use the port shape" group like HDMI that will threaten litigation unless you pay them to use the port would probably have prevented this kind of thing from being as widespread with USB-C as it is. While just about everyone doesn't want that to be the case (myself included), I don't see any other way of aligning incentives to make it harder to use the port/spec incorrectly than it is to make it correctly.