Well, not really because that part doesn't grant the US President arbitrary powers to perform any action that would result in regulation (for example, he is not given the power to go around killing random people even if doing so would effectively regulate international trade; he can't declare war on another country even if doing so would be the best way to effectuate regulation of trade with another country) it gives him the OBLIGATION to perform regulation, using the powers delegated to him.

If giving the US President unlimited and arbitrary authority as long as they can claim it was useful for meeting a legal obligation created by Congress were the correct interpretation then we need look no further than the "Take Care" clause of the US Constitution, where the US President is given the obligation to take care that all laws are faithfully executed -- which, with this interpretation, would mean that any action would be under the purview of the US President as long as they could claim at doing that action resulted in the laws being faithfully executed.