Is Basement Ceiling Insulation Really Needed?

Our home is a ranch with a full basement, about 1200 Sq Ft each level. The basement is unfinished, mostly below grade except for the last two rows / courses of blocks. The stove is in the basement and keeps the whole house warm, of course much warmer in the basement. The main floor, ceiling of the basement has R13 insulation installed between the joists, paper side up towards the floor. Sooner or later our plans are to finish the basement.

My thoughts on why the ceiling is insulated: I believe it was installed when the house was built as part of the design to get away with a cheaper - lower capacity furnace and AC unit, and maybe something to do with code about living space must be insulated. Basement not finished - not living space, and that since living space is only the one floor 1200 sq ft they could get away with only a 75,000 BTU unit, what is installed, instead of a 150,000 BTU unit or whatever the appropriate size would be for 2500 sq ft area, saving the builder/developer a bit of money on each house… adding up to thousands.

My question, is the insulation really required in the ceiling of the basement being that both spaces are conditioned area's, and once finished will it really make a difference other than providing somewhat of a sound deadening?

My thinking is to remove the insulation and use it to do the garage, and put the excess aside for the basement walls where I believe would do the most good. Also will the heat from the stove would be better as it will be also heating the floor above?

Any Thoughts?

Does you foundation have any insulation on the outside? I know MA code says if the foundation is not insulated the floors need to be. If your not worried about sound I would try to use it on the inside walls of the foundation.

I am not sure, the house was built in 86 but don't think there is any insulation, as a while back I had to dig next to the foundation about a foot down and didn't see any. And yes the inside walls to me would be the more preferable place.