Ok, I’ll bite.
Yes, there are organised fixed gear races, just like road races. They are called track races and they require a licence and a velodrome.
If you are talking about alley cats, yes, there are occasionally, but nowhere near as many as there were four/five/six years ago. Not only that, but almost none of them were fixed gear specific.
If you want to ride real fast in traffic on your fixie, you can do that at any time.
If you want to race in a competitive environment, you should go to DISC on a Sunday for a come and try it day. You might love it. Heaps of us were fixie kids before we got into proper racing.
Hope this helps.