I personally don't think theres anything wrong with not wearing golf cleats. Of course golf cleats do make you look a little more professional, I personnally believe they're not a must. There have been a few occasions when I've just worn my Reebok Hexalites (which are basketball shoes) and I did get a few giggles, but atleast I was comfortable.
You really have nothing to lose with cleats. The point is that they will never actually make the difference. If you have tennis shoes, they might cause you to fail if the conditions are bad. If you have cleats, you can't ever blame it on your footing.
Spikes DO make you look professional, and you'll instantly lose credibility if you show up for a competitive event without them. But the only time they really make a difference is when the course is wet.