Maybe I'm missing something?

Hell yes - the YAGNI part of it, which is the code generation, and the variable binding (which can be used for closures in the generating sub):

my $config = Config::Tiny->read($inifile);
for my $key (keys %$config){
   my $section = $config->{$key};
   my $record;
   tie my %h, 'Sub::Hash', $gensub, $record; # $record bound

   %h = %{$section}; # transforms all INI file values
                     # from this section into CODE refs

   my $result = getData( delete $h{SOURCE} );
   for $record (values %$result) {
       write_csv( my %out = %h );
   }
}
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This replaces an awful lot of code - which, I admit, could also be hidden in subroutines.

update:

Well, not so much really. Of course the subroutine table could also be set up as

%h = map { $_, $gensub->( $section->{$_} ) } keys %$section;
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But the point of the whole thing is to have all that encapsulated in a single tied hash, which is arguably not so great an a good idea.