For sure its poor instruction and not pushing harder to go through buoyancy drills with wet suits exactly how you'll be diving in open water, WAY before you hit the open water. To me, this is critical and its what's lacking in most OW courses because in most situations, the gear you wear in the pool is not the same as what you wear in the open water. In most cases, the OW instructor comes with gear for the pool, but when its time for OW, you've gotta rent gear. So all of a sudden you're unfamiliar with the gear and buoyancy characteristics of said gear, wet suits being the largest difference.
I feel doing a gear check-out prior to the open water dives is critical. I use to get my students to rent gear a few days before the OW and then we'd go through the gear and get some of the weighting done as a class in the pool, before hitting the open water. Just spending that extra time to make people more comfortable, makes a HUGE difference in situations like this. My students had excellent buoyancy control when leaving class, all because I spent more time with them in the pool practicing it, because it is a critical element. Once you can wrap your head around buoyancy and understand how it works, its very easy (even as a new OW diver) to use those skills in the OW.
In terms of BC vs no BC, I've tried both. I had a aqualung dual hose rig from the late 50's and a matching steel cylinder and plastic backplate. I loved that rig, get the weighting right and the thing was amazing. It was strange having no gauges outside of my diving watch for depth and a little "reserve" switch on the tank. Its kool to get that experience and understand how much more complex diving had gotten over the years. But in terms of having a buoyancy control device, you can dive without it, no problem. Its more difficult to control your buoyancy for sure and you've gotta really plan your dive and depth very well. I do prefer diving with a BC because you have MUCH more control, this is the reason why we started using them in the first place. But if you dive the same sites over and over again, there is absolutely no reason that you need a BC because by the time the tank is almost empty, you'll be a tiny bit positive anyway! Not suggesting that any new diver would want to do this, but anyone who is comfortable in the water and hasn't done this, its worth the experience.
Ohh and talk about a streamlined rig; tank, backplate, regulator, pretty simple!