Colin hit pretty much all the reasons as far as saving on utilities & the ease of maintenance when all the tanks are in one designated area. It's really no different than a laundry room or tool room, imagine having laundry or tool scattered in different areas throughout the house.
My fishroom is in a far corner of the basement, in a room that roughed out to 8'x16'. Well insulated, the room temp is about 78F, one large air pump runs all the tanks, saving money, an exhaust fan on a timer to keep humidity at a reasonable level. It's around the corner from the family room, behind the TV, so it isn't like I have to trudge through the snow to the back 40 to work with the fish. It is an escape of sorts for the dog & I, if the family happens to be getting on my nerves we can go downstairs, work on tanks, & chill. Part of any relationship is a certain amount of space, if you are with someone 24/7 they will get on your nerves eventually. It also makes it easier to work on the tanks at any time, sometimes I will go to bed early, and wake up quite early, such as right now. I can go down there & do whatever I want at 4am, if the tanks were scattered about the house everyone would kill me if I pulled that.
It gets pretty cold here in the winter, most everyone has their fishroom set up in the house, a few have them in an attached garage. This is another energy saving matter, heating a separate building can get expensive. Most people with enough tanks to justify a designated area breed fish to at least try to break even on the costs involved. A separate heated building increases those costs.
Colin mentioned locking doors, this is not just a good idea for theft, but also a safety measure for neighborhood kids. Kids will get into anything, I was a kid long ago, I got into plenty. You don't need any injuries to youngsters who get into your fish area, climb racks to see higher tanks, and bring down many gallons of water on top of them. My fishroom doesn't have a lock, but I can rig the doorknob so that you have to card the door to open it. I'll do this when friends or relatives are over with younger kids, last weekend was a good example.
Many people I know who have a fishroom also have a dog or two, this is a deterrent to theft, as well as a helper to deal with stray food that hits the floor. My dog will scratch on the fishroom door if I go down there & watch TV without opening it, he needs to go check it out.