There are at least RISC-V, OpenRISC, MIPS and maybe SPARC:

https://riscv.org/ https://openrisc.io/ https://www.mips.com/mipsopen/ https://en.wikipedia.org/wiki/SPARC#Open_source_implementati...

RISC-V was explicitly created to solve the problem of their being basically no open source architectures, and it's still fairly new, so it really is the exception that proves the rule.

Yep, but AFAIK they don't see much use in industry. There are people trying to change that, but they haven't succeeded yet.

MIPS gets used a lot in routers, it only went open relatively recently though.

I agree in terms of the equivalent of standard libraries. Ex: if you want a DMA engine, a PCIE interface, Ethernet, etc... you either have to build that from scratch, or buy IP from a vendor, there's not a lot of open source. There is opencores.org, but when a company is investing a lot in their own hardware design, then tend to want higher quality, or more recent/updated designs.

But the IC/hardware toolchain is a separate issue from the design itself. It's largely proprietary, probably due to the niche market and large R&D costs involved in some of the tools.