The smallest Lattice iCE40 are under $2 in volume, it may be "overkill" but also pretty tough to beat economically at low quantities. Especially keeping in mind one of the limitations of these MPW silicon runs is the parts you get are untested... reasonable in prototyping but an obstacle to scaling up to low volume production.

Dialog (nee Silego) Greenpak is a cheaper programmable option if you can find one that your design fits in. The design flow is a little more idiosyncratic.

Of course often the cheapest option these days for low-end digital logic requirements is to emulate your logic in a microcontroller, if you can get away with that speed wise. It might not feel very elegant but the economy of scale is tough to beat.

Personally it's analog and mixed signal design that I'd love to see cheap and easy custom silicon for... I've got a design with some DACs, analog switches, jellybean op amps, and a dozen-ish discrete transistors that would be really great to integrate and miniaturize, but it doesn't seem practical at ~10k volumes.