(De)soldering FPGAs is also very intricate, very high number of pins, high pin density make for a high error rate and low to no chance of simple rework. Also, the need for boards with a lot of layers to get that high pin count and density out from under the chip.

It is easier, faster and cheaper to start from one of the available devel boards and maybe even use them as production components for small batches

I've recently bought second-hand Xilinx FPGAs on Ebay for $250 each with list price of $3500. They come on boards that have an unidentified manufacturing fault. Salvaging and reusing the chips seems realistic using a budget vapor phase soldering setup (not attempted yet) but the challenge for me is designing or otherwise acquiring suitable PCBs to put them onto. I'm told that you can potentially find suitable PCBs on Aliexpress but I haven't looked into this in detail yet.

In other words, there doesn't seem to be much demand in the secondhand market, and you can potentially use that in your favor to take advantage of supply selling at steep discounts.