I had aweful pidgeon problems last year, so greedy and they come in flocks. Tried all sorts and really stressed me out, so I have converted an old Hamster cage into a small bird feeder and hang home made fat balls (coconut shells) inside and the little birds love it , I also hang a larger fat ball on the outside so the other birds can have a feed too. I have stopped feeding seed etc in seed feeders completely as the starlings & pidgeons ate it all in minutes and it is expensive now!
Since just feeding homemade fat balls it has been a real pleasure again, also my resident Sparrow hawk has taken two pidgeons recently so they have pretty much disapeared!
Great to see how secure the little birds feel inside the cage, while the Sparrowhawk was "dinning" the little birds kept feeding ! I cannot stop as Bluetits have started nesting in my 1 nest box and I love watching the birds!
Nature is harsh but I would keep feeding, if the pidgeons are too stupid to learn , then they will be lunch!