There's also the market for high performance things that need to be in-service upgradeable. I understand mobile base stations are a significant customer for large FPGAs, to enable deployment of new standards revisions/modulation schemes without a truck roll.

Pretty much. The problem set they're useful for is low-latency high-throughput stuff, and/or connectivity to high speed digital signals, for things that there isn't an existing custom solution and where you don't care about area or power consumption. That's not a huge market.

We do use them at my employer, a multinational chip company - but only in very small numbers, like one $50k board gets shared around project groups who use it for a few weeks each. Most of the work is done in simulation.