So, if you arrive at MDA, then one of two things have happened. You've reached MDA + 50 and have already initiated the missed approach. Or You've reached MDA + 50, have the runway environment in sight, and are continuing the approach with the auto pilot disengaged. (At my airline, we don't continue below MDA on the autopilot, is this done at other airlines? )
You've forgotten one scenario. In my company (also allowed by FAA), we are permitted to descend below MDA with *only* approach lights as reference, but *only* if the plane is in a position to continue a stabliised descent to the runway. (with AP disengaged)
In the above scenario, you legally cannot descend below 100' above TDZE unless the runway environs are in sight. If the AP has already started to round out the descent at MDA, the airplane will no longer be "stable", and you've given up the approach.
All that said, if you're continuing down a NPA based on approach lights alone, you are already rolling the dice IMO. Because it's allowed by regulation, my company has decided to give the option to pilots. Whether or not it is good practice in reality is another discussion.
Approach lights that extend out far enough to be seen at non-precision MDAs would most likely be installed on a precision runway. Those lighting installations provide good roll reference; vertical reference not so much.
I can see the above scenario working well to a precision runway with G/S out. An approach to 18 at BHM or most other NP runways, it would not come into play more than likely.