EZY and KL co-exist quite happily from MAN, EDI and GLA so why not BHX?
Don't forget BE flew BHX-AMS 4 or 5 times a day until their demise with healthy LF's. EZY are just picking up the re-developing demand for p2p,price sensitive travel to/from AMS whilst KL will continue to do what they do with connecting traffic.
Having said that, a recent Skyscanner search for BHX-BER gave EZY as an option via AMS on both legs with decent connections albeit without the ability to through check luggage. Might appeal to some and EZY serve a wide range of destinations from AMS.