setting include_prefix = $(prefix)/include/pike would mean the default is moved from being set in install.pike to being set in src/Makefile.
Yes, but as long as the default is not changed (including cases where you override $(prefix) etc), that in itself is not a problem.
--new-style should be unaffected by it, except that install.pike in line 2110 is: include_prefix=vars->include_prefix||combine_path(prefix,"include","pike"); which is rather odd. i guess this should be removed.
Why should it be removed? I don't see any particular gain with breaking command line compatibility with previous versions of install.pike, even if that compatibility is not needed by the Makefile.
(vars->include_prefix currently is always false anyways)
When called from the Makefile, yes. You could run it manually.