Will this lower the cost of manufacturing custom chips? Like fully manufactured PCB with components from JLCPCB is just a few bucks. Will the ASIC manufacturing process ever fall to that level?
Unlikely, manufacturing an ASIC is orders of magnitude more complex than manufacturing and assembling PCBs. At most this will reduce the price of whatever RISC-V chip is used on the board, and maybe increase the demand for more RISC-V chips in the future.
Google recently opened up a full 130nm ASIC design platform, including core cells, tools, etc... Google it, can't remember the name right now. They've even committed to manufacturing silicon for free for a few select open source / open hardware projects. I guess that's going to turn into some kind of low-cost shuttle in the near future. That's probably the biggest movement towards democratizing ASIC design the way that JLCPCB and others have democratized PCB manufacturing (and assembly, as you mention, although with a quite restricted selection of available parts). Kicad democratized PCB design and it's being successfully used for many projects these days.