BHX is a slight oddity as it is so marginal in terms of time.
When I used to do it fairly frequently I worked out that the train vs flight only saved me about 25 minutes. By the time I got to airport, checked in, wait at airport, take flight, wait for luggage, get train/taxi into Birmingham City Centre there isn't much in it!
That said, people still use the flight but would BE really be interested based on the pax number T3 get?