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In 1942, FDR asked Congress to implement a 100% tax on all incomes over $25,000 (around $375,000 today). This was backed by the unions and a clear majority of the voting public.

In fact, such a tax was not wholly implemented. It reached a maximum of 94% in 1944 and hovered around 90% for the next two decades!

This suggests it was a popular measure.

This, in essence, is a proposal for a maximum wage. Why was it implemented through the tax code rather than simply stipulating a simple ceiling?

Federal spending

Obviously, a tax has the significant advantage of providing money to the government, something that a ceiling simply does not do. Unsuprisingly, many presidents would prefer to have more money to allocate to their preferred budgetary purposes. In Roosevelt's case, this was World War II. Roosevelt all but said this explicitly in his April 27, 1942 fireside chat:

Are you a business man, or do you own stock in a business corporation?
Well, your profits are going to be cut down to a reasonably low level
by taxation. Your income will be subject to higher taxes. Indeed in
these days, when every available dollar should go to the war effort, I
do not think that any American citizen should have a net income in
excess of $25,000 per year after payment of taxes.

As always with politicians, it's difficult to say what his true motivations were. However, though Roosevelt is largely remembered for his social programs, he also was very dedicated to the American war effort, so this wouldn't have been out of character for him.

Inflation was also a concern. Roosevelt's treasury used this as an argument for the tax:

In late 1943, Treasury Secretary Henry Morgenthau asked Congress for
another tax increase. He framed his appeal, in large part, as an
anti-inflation effort. The new act, he argued must help stop
inflation. "[N]othing in the economic field can interfere with the war
effort as much as an uncontrolled rise in prices," he told the House
Ways and Means Committee. "An inflationary price rise is a source of
grave social injustice. It undermines morale and impedes war
production. It strikes at random without consideration of equity or
ability to bear the hardships which it imposes. Once it has acquired
momentum, inflation is extremely difficult to control, and leaves a
heritage of post-war stresses and strains that will haunt us for
decades."

Now, if a direct wage ceiling were imposed, companies, unable to spend that money on attracting more highly-paid CEOs, might spend it on competing for labor lower on the company totem pole. This would lead to more money in the pockets of somewhat lower-paid workers, which might be a nice thing for income inequality, but could lead to excessive spending and spur on inflation. I'm not sure how plausible this justification is, though: since the taxes were intended to be put back into the economy through military spending, it's possible they could have had the same effect.

If he just wanted to have a maximum wage of $1,000/hr, he probably could have just passed a law stipulating it. However, FDR was trying to create a maximum income, not a maximum wage. The government liming the total of dividends from stocks, interest from bonds and appreciation on homes via a legal maximum would be confiscatory and therefore unconstitutional. However, the government does have the ability to tax due to the 16th amendment.

This is also why Obama (and the Congresspeople working with him) did not add a fine for not buying healthcare - they created a tax (the Shared Responsibility Payment).

I'll leave aside questions about whether it's prudent to have such a measure in place. If you want to discuss that (and you seem to), I recommend creating another question.

It was most probably easier.

Setting tax rates is something that governments do all the time.
Yet, setting a maximum limit on the wage you could be paid-out, is a very tricky proposition. Especially in the US with its traditional high evaluation of individual freedom.
I guess it would have been legally straight impossible for FDR do impose a wage cap on private businesses.

I am interested in any more in-depth views of people who actually know the US law.