This does not sound crazy at all! Just ask any semi-serious runner, and you will quickly learn that having just one pair of shoes to run in is not very common. The normal amount for most runners is two to three pairs... but then ask the elites and they usually have five or more pairs at one time!
The number of shoes you should have at any given time for running depends on how much you are running and what style of running you are doing. If you are training for a marathon and logging 60 or more miles a week, you are going to wear your shoes out a lost faster than someone only running 20 to 30 miles a week. Have two or three pairs of the same road shoe to cycle through during the week will ensure your shoes last longer - and that you can actually make it through a whole training cycle running in the same pairs of shoes. This is actually important to your training because new shoes can take a while to break in. So you do not want to have to buy a new pair of shoes two thirds of the way through your marathon training, then suffer through possible blistering and the discomfort of breaking in a new pair of shoes so close to race day.
Shoes specific to the terrain you are running on also come in handy. If you run a few days a week on the roads near your house but then venture out onto the trails on the weekends for your long runs, it would do you good to own a pair specific to road running and a pair specific to trail running. This is because these styles of shoes are designed for specific functions. Trail shoes have a thicker sole and a better grip, to help keep you from falling. If you are competing in shorter distance races (like the 5k) then having a pair of "racers" (which are very minimal and lightweight shoes) will come in handy. But these are so minimal that they wear out a lot faster than your standard pair of training shoes so you probably do not want to run in these everyday.