That is how people were diving in the seventies, 50 years ago, when I started diving.
These plastic backplates are light and very comfortable, my actual BCD (an hybrid Coltri made in 1989) employs one of them. There are not significant buoyancy problem if used with a small-size single tank (at the time it was a 10 liters, 200 bar, steel, mostly), as the weight excursion full-empty is just 2 kg, which any decent diver can compensate easily with his lungs.
At the time there were just wet suits of limited thickness (my one was a 3mm Cressi), made of little air and a lot of neoprene rubber, so it was crushing much less than today's very soft neoprene suits. In substance, diving to 30m, at the beginning of the dive, with the tank full, one was negative by no more than 3 kg. Which did reduce progressively during the dive, while air was consumed and depth reduced, so at the end the deco stop was feasible in perfectly neutral buoyancy.
BCDs, at the times, were used only when diving deep, with ticker suits, and using twin tanks. For shallow recreational diving the BCD was entirely superfluous.
Now in many places (for example at Maldives) the BCD is mandatory for safety reasons (divers lost by the boat and floating for hours before being recovered), but during dive the BCD is still entirely useless, as usually no diving suit is required in those warm waters. So people simply use a very minimal-size BCD, just for compliance, keeping it empty for the whole dive, and using as a floating helper after surfacing, while waiting for the boat.
Here one of these plastic backplates: