along the lines of "Diagnose First, Repair Second".

OK, not trying to be ignorant, but if you have roots in a tile with that kind of fall, you had a blockage of some sort to precipitate it. - My opinion.

Thre are certain species of trees - willow/poplar/aspen that should be declared a noxious weed. They will get into tile. However, I have seen large roadside maples that practically grew on top of a tile without plugging it if the tile was working and would go dry. If the tile was damaged downgrade of the tree, and the water tended to 'sit' in the tile, eventually the roots would get into it. In our experience, we've not had a tile (with good grade and outlet) out in the field get a crop root in it without a blockage.

Example - we had a yard drain that conneced to a field tile which began to back up. We dug and dug, but could not find the problem. 'Acidentally' spilled an ounce or two of dicamba into the drain, and flushed it down with a couple hundred gallons of water. Two days later, the alfalfa in the field led me to the issue: a couple of corn cobs and some husks had fallen of the combine in the yard, would float in the catchbasin, and went out the outlet. They ran for 5-600 feet before they decided to turn sideways and restrict about 80% of the flow. Dug it up, repaired it, and put screens over the basin outlets to keep leaves etc. out of the tile. No problems two years later.

Good Luck,

Luke.