I assume the BBC paid a fee for the use of the facility. Maybe they piggybacked onto some testing or scheduled activities that were being done anyway. I'll bet once the location scout saw those huge doors close, the deal was set. ;-)

Similar large facilities exist at many national labs, and they are used only sporadically. For instance, in the Bay Area, NASA Ames has a very large (11 foot square) wind tunnel that can reach Mach 1.45 (http://www.nasa.gov/centers/ames/orgs/aeronautics/windtunnel...).

The inflatable bags that landed Spirit and Opportunity on Mars were tested in Mars air pressure at the Glenn vacuum facility: http://www.nasa.gov/centers/glenn/about/history/marspbag_prt... . Many spacecraft undergo "thermal vac" testing meant to simulate space conditions.

I seriously doubt they emptied the huge vacuum chamber for this experiment. Most likely it was used for some other experiment and it was very cheap to do this experiment as well. As to answer your actual question, because it's very televisual (this was for a TV show, after all) and sells well. It's something very simple, something (almost) everyone understands yet something almost nobody has ever seen. It's a powerful experiment for the general population.

But to answer a more general question. We shouldn't stop repeating experiments just because they were done before. The scientific method works as long as we keep reproducing results. Sure, this is a trivial result, but it's something every kid should have done by its own in the school physics lab.

Before they pump the air out in the video, the presenter explains what the facility was made for and is currently used for.

The presenter was wearing a wicked smile when the feather hit the box.

Dropping feather and hammer isn't the only use of vacuum chamber