Why have the 50% setting and no setting any lower if it wasn't better for the battery?
You would set the charge limit to 50% if you're planning to plug in then head out of town for months at a time.
For daily driving, set it to 80% and you'll be fine. You gain nothing from setting the battery to 50%.
Speed, temperature, cycles and percent full can all be bad for the battery.
That's sorta true, but you're incredibly unlikely to hit the ranges that are actually bad.
Speed: You'd have to supercharge from a low SoC to a high SoC several times per week for the charging speed to matter.
Temperature: The car won't let the battery get hot enough for it to be bad for the battery. When it's really cold out, you'll notice a dip in performance, but drive like a normal person and you'll be fine.
Cycles: Don't worry about this, you'll be fine.
Percent Full: Don't charge to 100% and then let the battery sit there for days like that. If you're going on a long trip, time the charging so it gets to 100% around the time you want to leave. Charging to 80% on a regular basis is perfectly fine.
I also just charge it on the regular 120 because that's all I need and it's better for the battery.
This is absolutely false. Trickle charging has no real benefit to Li-Ion batteries. 40A at 240V is plenty slow enough to be divided up between the 7000ish cells in your battery pack.
Charging at 120V will make your electric bill be higher than you'd expect. Your battery pack is 300VDC and needs to be charged with a higher voltage than that. 120VAC yields about 170VDC. Doubling the voltage halves the current, and you end up with some losses in the converter circuit. 240VAC makes about 330VDC, which at that point can go straight into the battery pack.
Another good thing about hte higher charge current is that it will keep the battery warm in the winter months. If you schedule your charging to start about 4 hours before you plan on leaving, you won't have reduced regen and acceleration.
Tesla's battery management system (BMS) knows what's best for the battery and will do it's best to prevent the battery from being harmed. Set the charge limit to 80% and enjoy the car.