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One thing I've wondered is to what extent does discrete logic "scale proportionally" to integrated logic.

I mean if you make a big machine out of these things, are the trade-offs you make regarding e.g. signal fanout and propagation delay similar to those made in an IC that did the same computation?

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One of the biggest issues is complexity. Sure you can make some fairly complex things within an FPGA fabric, like a CPU or GPU. However, you'll see a slow down in two areas. The first is routing, whereas an IC would just have a wire between two components, FGPAs have to route further and through different interchanges. Second, components can only be built up through the basic components of the FGPA, typically a LUT and FFs. The more complex components, the more small parts. Another aspect is memory; blockram works decent but it's an explicit design choice, DRAM via DMA is also a pain too.

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