That is quite expensive. Obviously you need to physically add the register to the chip.
After that the real work comes. You need to change your ISA to make the register addressible by machine code. Pdp11 had 8 general purpose registers so they used 3 bits everywhere to address the registers. Now we need 4 sometimes. Many op codes can work on 2 registers, so we need to use 8 out of 16 bits to address both where before we only needed 6. Also pdp11 had fixed 16 bits for instruction encoding so either we change it to 18 bit instructions or do more radical changes on the ISA.
This quickly spirals into significant amounts of work versus encoding results and error values into the same register.
Classic worse is better example.
There are quite a few registers (in all the ISAs I'm familiar with) that are defined as not preserved across calls; kernels already have to wipe them in order to avoid leaking kernel-specific data to userland, one of them could easily hold additional information.
EDIT: additionally, it's been a long time since the register names we're familiar with in an ISA actually matched the physical registers in a chip.
By 1983, operating system vendors designing their APIs ab initio were already making APIs that just used separate registers for error and result returns. Sinclair QDOS was one well-known example. MS-DOS version 2 might have done things the PDP-11 way, but by the time of MS-DOS version 4 people were already inventing INT calls that used multiple registers to return things. OS/2 was always returning a separate error value in 1987. Windows NT's native API has always been returning a separate NTSTATUS, not doubled up with anything else, since the 1990s.
Too, I'll read any post that mentions OS/2; I loved that OS so much as a user. Partially also because some of the REXX I learned in college could be put to use.