Gordon Shumway wrote:

Why would you want to install the base trim off the floor? That would
increase the difficulty of the trim installation for no reason.

In a production house, base molding is frequently installed before the final
flooring (carpet, wood, tile). This lets the painters come in a spray the walls
and ceiling without having to protect the floor. You don't have to install the
base trim this way, but it means the trim has to be painted separately, and you
have to touch up all the seams.

Most homes have base moulding installed on the floor (underlayment)
for all carpeted rooms. Any rooms using something other than carpet
such as hardwood, tile or sheet goods would be installed before the
base moulding. The base moulding would then be ripped to a width that
will line up with the height of the moulding in the carpeted rooms.

You can install carpet flush with the base trim, but it makes stretching very
hard, means the edges have to be perfectly cut and makes the base trim look
short. Far better to use the gap under the base trim to hide the edge and allow
for stretching..

Ripping molding to match height? Only if the cost of labor is not a concern.