As a follow on from How do I adjust our "default" domain I am about to setup 301 redirections from a selection of TLD to our recently selected default domain.
Currently ALL of our TLDs point to the same IP, a single host, and I had initially thought to setup the 301s on this hosting. In comments by @ThomasClayson in the above linked question, he suggests purchasing new hosting purely for the 301 redirects.
What would be the advantage to us in purchasing new hosting purely for the 301 redirections? Why not redirect on the same host? (Or does this not work!?)