It's an entirely new hull, suspension, and powerpack. All that adds up.
"Strategic mobility" is generally used to refer to the ability of a force to be deployed in and out of theatre. A frigate possess a high degree of strategic mobility as it can sail into the South China Sea, sail right back out, and be in the Gulf fairly quickly, with a limited cost in terms of resources (essentially, the gas it burns to get there).
The Stryker Brigade was originally envisioned as a strategically mobile formation. Something that could be fit on C-17s and C-130s and be flown into a theatre for quick effect - the stated goal was 96 hours. Vision never really made it to reality though. The Strykers are too large and heavy. RAND
did a study and found that the deployment time was generally 2-3 weeks, and that this would consume a lot of C-17s (not C-130s) to make it happen.
In the CAF context, tanks will not significantly affect the strategically mobility of a CMBG as a CMBG is not inherently strategically mobile. We don't have the capacity in our air transport fleet to move a significant land force element. If I recall correctly (a loadie can sort me out) you can get 1x MBT on a C-17, and 2x LAVs on a C-17, so you ain't getting much forward deployed very fast. The most effective way is to move by ship, but when it comes to a large transport ship, the difference between an MBT and LAV is negligible.
Now the argument has been shifted to arguing for the LAV/Strykers "operational mobility." This is viewed as the ability of a force to move around once in theatre. The common "inflection point" that is often cited is Kosovo in 1999, where heavy tracked NATO forces were busy offloading and plodding towards Pristina only to find that the wheeled BTRs of the Russians had beat them to the city. A Stryker Brigade was supposed to offer a double whammy of strategic and operational mobility; it could get to the theatre fast and move around quickly. It only is able to live up to the latter (for good examples of this, see the actions of US 2 Cavalry Regiment, a SBCT, moving about Europe in the last few years as part of NATO deterrence).
A CMBG with tanks will lose that inherent mobility as tanks can't move far on their own before suffering maintenance issues. This is why transporters are usually used to operational transport MBTs.