I will ALWAYS remove my BH for most operations -- mowing, blowing, bucket loading/scraping, etc. Unless I plan to lift heavy stuff with the FEL, the BH is off. In actuality, the only time I put the BH on is when I plan to use it (and in that case, the FEL always goes on, too.)
Not sure about the set-up with newer GCs, but on mine, I can drop the BH in about 8 minutes; putting it back on varies, depending on how close I get lined up the first time, but extension hoses on the 3 lines really helps, as I can be connected to the BH while still 2 feet away from it.
With the hydraulic extensions (which I leave on the BH), I can easily drop it to the ground -- a firm spot/stump/concrete pad-- and retract the stabilizers all the way for storage, then a small tarp (I use an old shower curtain) for a cover. I suggest you practice doing that, it does get easier with repetition-- and with the BH off the tractor is just much easier to maneuver and control.
PS: If you DO leave the BH on for mowing, I believe you still have to disconnect the hydraulic lines to it and connect the two recirculating lines (just as if the BH were removed) in order for the 3PH/MMM to raise & lower.