It only shows that the Pythagorean theorem holds for that one particular set of side lengths. A mathematical proof requires that you show it is true for all possible side lengths.
An analogy would be that I take two equal-length sticks and say "given any two sticks they will be the same length". I have an example (the two sticks I'm holding) but this does not amount to a proof of my statement (and the statement is obviously incorrect).
It’s interesting to wonder if a contraption might be built whereby some slider adjusts the sizes of the two smaller squares, while maintaining the right angle (i.e. keeps the corner on a circle with the hypotenuse as diameter). It would be much more mechanically complicated and harder to build, but pretty awesome.
That's easy enough, but it changes the total area, which means some kind of drainage is required, which complicates the demonstration of equal-area squares.
As long as you don’t change the size of the large square, the total area of the two smaller squares must be the same. That’s just a restatement of the Pythagorean Theorem.
An analogy would be that I take two equal-length sticks and say "given any two sticks they will be the same length". I have an example (the two sticks I'm holding) but this does not amount to a proof of my statement (and the statement is obviously incorrect).