I started diving after the BC revolution, but for money sake, my first diving (after cert) was done with a back plate and no BC. This was actually a fortunate move, as I had to learn how to weight myself properly. I just got used to keeping track of the pounds each time I changed to a different tank or added, or removed a pony bottle or other piece of equipment.
After a couple years, I eventually got the money together for a good BC setup and dove that for many years, even doing quite of bit of tech. I got tired of all the heavy tech gear and started a process of slimming things down, and found that the less I had, the easier and more enjoyable my dives were getting. I eventually got rid of the BC and started diving just a simple tank and harness like I had in the beginning. I hadn't realized just how good I had it when I couldn't afford the BC. I've been diving without BC now for a little over 10 years now and have little interest in going back. It's the most fun I've had scuba diving, so I hope you can enjoy it the same as I have.
For me, I won't even consider using a BC unless I'm diving over 3mm of neoprene head to toe and double thick over the chest. I've often dove up to a single 120 cubic foot tank no BC; I had no issues with that. Other conditions are generally not a factor. I have better diving ability without the BC, so rough water, strong currents, I'd rather not have the BC as I see it as more of a liability than an asset. As for those who say you'll be crawling on the bottom if you don't have a BC, they are ignorant. I generally display better buoyancy control and ability to hover over the reef than the others who are using BCs. The main reason, I pay more attention to my weighting.
So, when is it safe to dive without a BC? Any time you have taken the effort to accurately plan and account for your weight and buoyancy shifts over the course of your dive. Rules of thumb, not more than 3mm full neoprene and a single tank non-decompression dive are easy to get the accounting right and conduct safely. More neoprene is possible, but takes a bit more attention to depth profiles.
My advice is to start easy and work your way into it. Do some test dives to establish a baseline, and then track the weights as your suit, tanks and gear changes. With a little practice, you'll develop a library of info to take the guesswork out of your planning. I shoot for being neutral at 15 feet with shallow breathing when the tank has 500 psi. That will allow me to do my safety stop without having to do anything to hold myself down. I consider this to be the ideal condition for diving without a BC. At the beginning of the dive, I'll breathe a little higher on the lung to maintain buoyancy. It's easy and comfortable. I don't even think about it anymore. It's automatic for me.