This is almost more of a legal question than a history question, but I'll address the legal history aspects of it. First off, if Congress were to pass a new Volstead Act banning the sale of alcohol, there is no doubt they would have been successful but for the 21st Amendment. So, while there are reasons to prefer an amendment over a simple law (harder to repeal, for example), I think the bigger reason is simply this: A Constitutional Amendment will be upheld by the US Supreme Court, while an act of Congress would be more in doubt.

Congress has the power to regulate interstate commerce, not all commerce. Therefore, the ability to regulate internal state commerce was somewhat in flux during this period. Some laws were upheld, but quite a few were struck down. In the Shreveport Rate Case, the Supreme Court upheld the regulation of in-state train prices of trains that crossed through states (basically, they were interconnected and you couldn't regulate interstate commerce without regulating this in-state commerce). On the other hand, a law banning the selling of items made through child labor was struck down. Likewise, regulations on manufacturing that are disguised as taxes, such as in Carter Coal were struck down.

Carter Coal happened in 1936, one year before the Marihuana Tax Act was passed. However, the Court's jurisprudence was far more favorable towards federal regulation of commerce even then than they were in 1919. Very soon after, the floodgates would open and, by 1942, virtually all federal commerce regulations would be upheld.

So the simple answer, from a historical perspective, is that Congress felt laws would be more likely upheld by the Supreme Court in 1937 than they did in 1919. They did start somewhat cautiously, using their tax power rather than commerce power to ban it. It was only in 1970 that Congress used the Interstate Commerce clause to ban Marijuana, in response to the tax act being declared unconstitutional because it violated the Fifth Amendment.