Honestly, I wouldn't have pets without one, and you can put the block in if and when you don't want them using it. We have always had an older dog or cat that showed the puppy(s) how to use the door. It eliminates potty "accidents" in the house, and you don't have to worry about them holding it all day while you're at work. The door I like the best comes from Pet Doors USA and is the 2 door PlexiDor with upgraded hinges. Our 5 yr. old Ruggles comes thru the door at what seems like 50 mph. They make a wall mount door, too!
Regarding neutering, we have been pleased with doing it at 6 mos. It is easier on the dog, they recover faster and still get as big and develop the same. Whether they hike their leg (Mack does, Ruggles doesn't) seems to me to be more connected to temperment than what age neutered.