With some adaptive programming in the TV, it seems like burn in could easily be avoided.

That test is being run with pixel shift active on a low brightness, then being allowed to run the pixel refresh once a day. If the TV was going to stop burn in, it would have done so.

It did not.

I have a 55" 2015 OLED that I use as my computer monitor and frequently game on. I have had no issues with burn in or image retention at all. I also have a 2017 65" OLED that I haven't had any issues with either.

I just simply don't believe you. I'm sorry, but OLED technology doesn't work like that, and you're either not using an OLED or lying because your computer monitor would have burnt something in the first year. 

I did not mean that that software was good enough yet, but software that can recognize still images that may potentially damage the display is certainly doable. I'm just saying that software may eventually very well be able to overcome the shortcomings of OLED pertaining to burn in.

Ah, in that case it's unlikely. Samsung is making great strides with putting self-emitting diodes on QLED panels, so we're more likely to see the "Quantum OLEDs" my company's Samsung rep keeps talking about before OLED burn-in is entirely prevented. That will be a good thing, too, since QLED doesn't burn in and has much more color than the OLEDs.

I have yet to see a QLED that looks as vibrant as an OLED though...

Well, as far as objective testing is concerned, they have significantly more color volume (I forgot the add "volume"), but the big deal about the theoretical quantum OLED is self-emitting diodes with no burn-in.

Maybe it's just our set-up at work, but of all the TVs we have on display, none of the QLEDs come close to LGs OLEDs.

You may not want to hear this, but wait till next year.  Over the next year OLED will take over the market.  OLED is definitely worth the added cost, but like you said it is a little pricey right now.  One cool thing about OLED is that the benefit is immediate.  You don't have to have any other special tech to enjoy a drastically better picture.  Unless you have a full 4K player and 4K media, having a 4K TV is just not worth the upgrade. We will also hear more word on next gen consoles which will like be fully 4K, not pseudo 4K, from time of launch.

It depends on your situation though.  Do you have an extra $600 laying around that you have absolutely no other place to put it?  Are you going to have a definite excess of $1000 next year to play with?  If the answer is yes to both questions, then do what you want.  You can always sell the 4K TV you buy this year, next year, or use it in another way.  If you are limited on cash though and will be over the next year, do what I suggested first and wait.