Is train station - or even railway station - used that frequently, anyway? In my experience, THE station invariably means the place trains, not buses, stop at. If someone I was arranging to meet and go for a few beers with said to me, "Let's meet at the station at eight", it wouldn't even occur to me that I should head for the bus station.
Train station started life as an Americanism. As such, the reason some of us have adopted the phrase is because we decided we liked it and found it useful. That's what we do with all such 'imports'. Perhaps, as suggested above, it was because it is shorter than railway station.