You are asserting that any time you interpolate a compiled re into another, it just stringifies the first anyway, and re-compiles the whole thing?

That's no assertion. That's how it works.

I had always assumed that it copies the compiled bits and does not need to re-process it.

No, that's not really possible to do (think for instance paren counts - or consider this: $q = qr/x/; $r = qr/[$q]/). It only works in this case:

my $qr1 = /pattern/;
my $qr2 = /$qr1/;
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Use use re 'debug' and you will see what strings are being compiled.