Threadripper 1950x comes with the same core count, more memory channels, more PCI-E lanes and more memory. You can grab one for $499 from amazon.
So you're not going to save more then a few bucks but get a slower and outdated CPU.
Note: I have a TR cooler running on my AM4 board (custom loop though so not completely comparable) and there is more than sufficient space to place it.
In turn, I misunderstood your reply to @lhoff, because in that context, I read it as a rebuttal of the idea that TR parts being expensive by suggesting an AM4 mobo + TR4 cooler as substitutes on a 1950X system.
My 4790K feels so outdated now...
I wouldn't make the assumption that AMD could sustainably sell that much silicon at that price point.