emacs{-app,}-devel +nativecomp: runtime native compilation fails on Big Sur 11.1

[amake (Aaron Madlon-Kay)]

After updating to Big Sur 11.1 I find that the runtime native compilation (shown in the *Async-native-compile-log* buffer) fails with errors like the following:

Compiling /Users/amake/.emacs.d/elpa/use-package-20201110.2133/use-package-core.el...
ld: library not found for -lSystem
collect2: error: ld returned 1 exit status
libgccjit.so: error: error invoking gcc driver
Debugger entered--Lisp error: (native-ice "/Users/amake/.emacs.d/elpa/use-package-20201110.21..." "failed to compile" "/Users/amake/.emacs.d/eln-cache/28.0.50-x86_64-app..." "error invoking gcc driver")
  signal(native-ice ("/Users/amake/.emacs.d/elpa/use-package-20201110.21..." "failed to compile" "/Users/amake/.emacs.d/eln-cache/28.0.50-x86_64-app..." "error invoking gcc driver"))
  comp--native-compile("/Users/amake/.emacs.d/elpa/use-package-20201110.21..." t)
  eval-buffer(#<buffer  *load*> nil "/var/folders/m1/c0nhy2412p1_5bbn8t5hzs000000gn/T/e..." nil t)  ; Reading at buffer position 7282
  load-with-code-conversion("/var/folders/m1/c0nhy2412p1_5bbn8t5hzs000000gn/T/e..." "/var/folders/m1/c0nhy2412p1_5bbn8t5hzs000000gn/T/e..." nil t)
  command-line-1(("-l" "/var/folders/m1/c0nhy2412p1_5bbn8t5hzs000000gn/T/e..."))
  command-line()
  normal-top-level()

I believe that this was caused by the update to 11.1 (I'm pretty sure it was working fine on 11.0). I've tried recompiling but it didn't help.