[PapaBear3625]

They're missing the obvious reason---a road that high with deep side ditches would make ambushing a passing Roman column from the woods very difficult.

Besides that, it allows water to drain away so the road stays dry, is not flooded by heavy rains, and also snow would tend to be blown off by winds into the ditches.

[Lancey Howard]

Besides that, it allows water to drain away so the road stays dry, is not flooded by heavy rains, and also snow would tend to be blown off by winds into the ditches.

Precisely.
No doubt the elevated road was built by having two columns of laborers looking across at each other an equal distance apart, who shoveled dirt into the middle, between them, thereby creating the elevated road and the drainage ditches at the same time.