Won't it amount to the same thing as a heat source anywhere else in a room, with convection and radiation?

Modern heat pumps are three to four times more efficient in their use of electric power than simple electrical resistance heaters.[1]

I have a 7.1kW heat pump, it uses a little over 1.79kW of power generate that heat, so a thermal efficiency of 3.96:1. Any light bulb, whether it's incandescent or CFL or LED produces heat a 1:1 thermal efficiency.

1. https://en.wikipedia.org/wiki/Heat_pump

Do many people have heat pumps? Most people I know in the Midwest make 100% if heat from burning natural gas. So in the winter not a huge loss (just the delta on cost between electricity and natural gas). In the summer obviously you pay double..

Heat pumps / reverse cycle air conditioners are very popular in Australia, but the temperature here is fairly moderate, even in Tasmania where I live there are few places where it's below zero for more than the over night period. Heat pumps don't work so well sub zero.