You said to take the battery out while using the AC adapter. I like to keep my CPU functionality and not worry about unplugging it and losing all the work. It is also well known that for people who use the computer for long periods of time that if they continuously cycle the battery without letting it sit charge it is going to die an early death. This is what I did with my first battery for this computer and it died in 3 months. Obviously it was probably a fluke, but it is an example. Batteries have limited lifespan in terms of cycles. If you are on the computer all the time you don't want to cycle it too much or you'll cut that battery lifespan short.
I am not encouraging constant charging. I do not recharge until I hit 15-20% usually. I do a complete discharge about once per month. For those that want convenience, buy a laptop cooling pad which will keep the battery at friendly temperature when on ac mains power. I personally do not remove my battery on my Mac Book, but my battery still has 100% health after 1.5 years. I use my Mac Book about 2-3 hours per day on average. If I were using more like a desktop, I would remove the battery. And considering incentives, it does make sense for Apple to be very "conservative" on the battery advice as it makes money when you need a new one or just buy a new laptop