There is a long standing rumour that back in the days of Stelios easyjet had a meeting at Birmingham with a view to making it a substantial base. The story goes that the BHX administration at the time were very dismissive (some say downright rude) of what was the low cost revolution in it's relative infancy and in no uncertain terms told easyjet that Birmingham's future remained firmly with it's British Airways base. The rest is history.
As said that is purely a rumour but if there is any truth there it could go some way to explaining why easyjet ignored Birmingham for so long.
When British Airways closed their regional bases Manchester was in a very similar predicament to Birmingham but since then it looks to have realised the massive potential that easyjet offer and now has a very successful base. Why Birmingham cannot, or will not, do something similar remains a mystery. BHX is now in a situation where many routes are only covered by the full service airlines or Flybe and can be vastly more expensive than flights at other airports and as a result may be losing a huge amount of the city break market. I've heard it suggested that easyjet are more than happy to mop up Midlands travellers from their other bases with Luton being the main beneficiary by far. There may also be an element of protecting some of the full service airlines.
It has been suggested elsewhere on this forum that the previous CEO was extremely focused on getting BA back to Birmingham, maybe he/they thought that an easyjet base would end that vision for good? Hopefully the new CEO will realise that any return of BA in a major capacity is pure fantasy and do what it takes to get easyjet in.
Until then I will look enviously down the M5 at routes such as Seville, Reykjavik, Lisbon and Olbia all of which are unavailable from Birmingham 🙁