A tyre carrier is for tyres that are too big to fit in the usual spot under the back. If your tyre still fits there then leave it there.
You can always find another spot to squeeze in an auxiliary tank or whatever.
Besides, when last did you need to change a flat? I carry a tyre repair kit behind my drivers seat and if I feel or hear I'm getting a flat I get out and fix it right there and then without taking the wheel off. The spare is just for emergency if I totally destroy a tyre.
06 Mitsubishi Colt 2.8i turbodiesel Clubcab
(Americanese translation: L200 crewcab, or a truck version of a Pajero Sport)