It's not the depth of the roots as much as their texture. Fibrous rooted
trees, such as those aclimated to wet areas tend to get into pipes more than tap-rooted species which are adapted to upland conditions.
Another tip on your pussywillow, IIRC, as they age the upper branches will tend to canker and die, but as long as you watch them, and prune off below the canker they sprout well and you can maintain a nice
plant. Don't be afraid to lop.
You can do the same thing with the upright Italian poplars. Just Cut them below the canker area before it gets to low and they'll grow back like crazy.