If it means designs inside an EDA environment, design get submitted and shows up realized, then that is possible now. And it's not all that expensive. eFabless chip ignite is quoting ~$10K for 100 QFNs in 130nm. That's getting into beater car territory. https://efabless.com/chipignite/2110C

If it means actually fabricate then I think there is no way because a DIY won't have the scale to compete on price and they won't be able to bring any custom processing step to justify being at boutique scale. Think about PCBs. We used to make them ourselves with chemical etch. Now I don't even use breadboards because a custom bare fab is $5 and the components cost more than that. I also get a much better electrical result, and it doesn't fall apart if I look at it funny.

The main problem with ASICs is the amount of skill/time that it takes to do it right. Floor planning, track planning, closing timing, etc. etc. on an ASIC is much harder than an FPGA. You don't even have to do half those things on an FPGA.

With an FPGA one can almost get compile and go if you're willing to be loose on area and performance. ASIC CAD tooling is no where near that at the moment. Closed or open source.