I think it's possible on a 1980 model to remove the key from the bike with the lights still on.Someone will come along and say if that's so.
Yes that you can certainly be do that on the early model - been there done that several times. A good battery can handle this for a few hours but overnight would likely flatten it.
With all the expensive bits already replaced including the battery a good mechanic with a voltmeter should have been able to sort whether the battery is being charged very easily.
1. Before I did anything I would start with a fully charged battery and I mean fully charged. Trying to do any diagnostic work on a partially charged battery can lead you astray.
2. Leave the battery overnight for the surface charge to dissipate and measure the voltage with an accurate meter. A new wet type battery should have a good 12.6 volts and a the other types a little more maybe 12.7 - 12.8 volts.
3. Start the bike and measure the voltage at the battery while gently reving the engine to 3000 RPM. The voltage should rise to at least 13.8 volts but not more than 14.2 volts.
Come back and tell us what voltages are measured on the bike.