"by reason of their control of the carriers" was the necessary nexus which allowed the court to rule as it did.
The court was saying that because there was a connection, a relationship, between the interstate and intrastate rates by a carrier, Congress could step in a regulate the overall rates. The predecessor to "substantial effects" if you will (the court used "substantial relation").
Nope. They said:
"by reason of its control over the interstate carrier in all matters having such a close and substantial relation to interstate commerce"
The relationship between intrastate and interstate commerce is irrelevant. The only relevant relationship is between the carriers and interstate commerce - in all matters, intrastate or otherwise.