If riding is something you have to do and you have only one bike, you are a slave to it. You have to ride and the tire is flat. You HAVE to fix it. A wheel out of true, a headset less than perfect. With multiple bikes, you can grab another.
I've done both (though I have always had 2 bikes, one a beater fix gear). In my racing days, when I got bumped by a car and wrecked my wheel, I had to work the the next day till after lunch instead of taking my usual midweek day off to ride, then stay on at the shop to rebuild the wheel so I could get out the next morning early and ride my 120 mile midweek ride and be back at work at 2. All winter my fix gear was my only transportation and I spent many evenings doing repairs to have a bike to ride the next day.
If riding is just a past time, more than one is far less necessary.
Ben