Why not? If my neighbor gets planning permission to do something, doesn't that increase the chance that I might also get such permission in future? If so, doesn't that increase the value of my house?

Only 1/N homes would be converted to apartment complexes. If 1/N * (gain for selling home to build apartments) < (average loss in home values) it's a net loss for the community.

So, the real question is how much home density are you are adding. Further, density can get vastly higher as people would be adding 20 story buildings not just smaller apartments which means most homes would not be converted.