Pigeons keep chasing away better birds nesting above my window!!!

There's this corner above my window covered in anti-bird spikes that provide perfect support for nests.

Now, I have nothing against any bird nesting there except the darn pigeons. They're loud, annoying, fighting in front of our window at dawn, and once they leave the stupid mites migrate to our house until we organize for someone to come remove the infested nest.

Last year some jays built a nest there and we were so happy - until the pigeons chased them away and moved in.

Now we have magpies nesting and I hoped the shape of the nest would not be tempting, but in the past few days I've seen pigeons around the nest all day and heard their stupid flapping and fighting at dawn. I haven't seen the magpies in two days and I'm worried they chased them away again.

What can I do against these bullies? Why are they doing this? Their obese bodies can't even enter the magpie nest so are they just territorial?

Any tip to fight against them is welcome! And please no pigeon apologists here, I will never hurt them but I also think they're getting way too cocky. This is happening in a city btw