Cool'n'all as that is, by deferring the construction of constants to runtime, you disavail yourself of various compile-time optimisations that Perl has.

Even the very act of interpolating a read-only variable is an active pessimisation, as whilst perl will enforce the read-onliness, Perl does not (cannot) know that it need not re-interpolate the variable every time it is used:

use constant CONSTANT => 10;;

Internals::SvREADONLY( my $READONLY = 10, 1);;
[Type of arg 1 to Internals::SvREADONLY must be one of [$%@] (not scal
+ar assignment) at (eval 11) line 1, near "1)"

$READONLY = 10; Internals::SvREADONLY( $READONLY, 1);;
++$READONLY;;
[Modification of a read-only value attempted at (eval 13) line 1, <STD
+IN> line 6.

cmpthese -1,{ 
    a=>q[ for(1..1000){ my $string = "the constant is " . CONSTANT . "
+\n" }  ],
    b=>q[ for(1..1000){ my $string = "the readonly is $READONLY\n"; } 
+       ],
};;
    Rate    b    a
b 3893/s   -- -46%
a 7236/s  86%   --
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A small a difference as that may be; it is all those avoidable small bits that add up.