Fine fibrous roots throughout my Garden, How to control or get rid of?

You do really need to know what grows from the roots before deciding how or if you have to deal with them.

Just because root crops do not do well is not necessarily because of the roots in the soil. It may be that your soil is too heavy/clay like or not tilled deep enough.

Or maybe the soil needs amending. Have your soil checked or buy a tester kit and do it yourself.

Make sure your soil is the proper ph and if it needs any specific nutrients.

Find out what the roots are for sure. To me poplar roots don't flash as fine or fibrous.

The problem is that those tree roots wrap around the roots of small tress or shrubs and shocks them