The function that is called, when just typing x in the REPL is here. One could hack this to optionally have show(IOContext(io, :limit => false), mime, x).
While this could be handy in interactive use, it would require a global state, which would complicate a lot of other things (eg reproducibility, testing, threads, …). Generally, global states are avoided if possible for these reasons.
Having this implemented with IOContext with an easily accessible API is probably a better solution.