It's very easy to show that the tank's surfaces and filter, not the water, hold the vast majority of the beneficial bacteria.
Take the water from cycled tank and put it in new, sterile tank with a brand new filter. Replace that water in the existing tank with fresh water and dose both tanks with the same amount of ammonia (only do this if both tanks contain no fish!). Test for ammonia after 24 hours. The new tank will show little or no decrease in ammonia, while the existing tank will show significant decrease.
When you transfer 'old' water, you're mostly transporting pollutants, organic metabolites and end-products of a number of biological processes. Why would anyone want to do that?
Jim