Hmm, a few thoughts, regarding “turning the bulb on an off many times a second”. I’m not surprised it works, why should it not? But...
First, I believe led controllers often already modulate on/off at a rapid rate, using a pulse width modulated signal to control brightness. That is energy efficient and also maintains a more consistent colour, compared to simply reducing the current through the device. Maintaining PWM to control brightness, alongside some other modulation to effect data tx might be tricky.
Second, some led installations may have no “slack”, being expected to provide the full 100% intensity that the source can provide. As soon as you start modulating the signal you will introduce periods of darkness interspersed with light. That can be made to happen very fast, so the human eye does not notice flicker, but it must reduce overall intensity, which might well be an issue.
Just my thoughts.