Do more damage taking it down than leaving it where it is. Soil often shrinks when trees are removed and cause subsidence where the roots were doing no harm.

No, Hank - palms really don't have a huge root system like ordinary trees, and rarely interfere with foundations, although, as Owdboggy says, removing them can cause disruption to hard surfaces nearby.

Palms are much safer than other trees in tight spots: they completely replace their root systems every few years, and the old roots don't expand the way more normal trees' do

Thanks guys, my daughter wasn't worried but I was a bit perturbed myself,