[ifinnegan]

No. Highways have cross streets.

[Dr. Sivana]

Highways have cross streets.

Source?

From Century dictionary:

highway
/hī′wā″/
noun
1. A public road or passage; a way open to all passengers, by either land or water.
2. In law, any road or way, whether for foot-passengers, beasts of burden, or vehicles, or all, over which all persons, as members of the public, have a right to pass.
3. Figuratively, a common or easy way or course

If you can find a dictionary or other source that requires "crossroads", post it here.