Once I got in to quite an argument with an esteemed, internationally recognized concert-pianist...He thought if it didn't "make a difference" Schumann whould not have written it that way.
This sort of thing can be tricky. I've seen people get unreasonably angry about such issues.
There are a few points to bear in mind.
1. In live performance, your gestures are visible to the audience. For a concert, things do need to look
right as well as sound right. The clearest example I can think of is the opening of Beethoven's Hammerklavier
sonata. You'll remember that it starts with a low bass note followed by a chord two octaves higher, both to be played by the left hand. To see
a pianist perform this rapid jump is exciting! Of course you could play the chord with the right hand instead, and it would be safer, but it wouldn't look so good. Likewise at the start of Liszt's Dante
sonata, the left hand octaves could be played with two hands, but it wouldn't seem nearly so dramatic in live performance.
2. Distributing the notes differently between the hands will sometimes make it easier to achieve a particular voicing. Of course the ideal pianist will be able to achieve any voicing with any fingering. But there's no harm in making things more comfortable sometimes. When the hands are interlocking (as so often happens in Schumann) it may be a clue that the composer was more interested in the inner voices--that you should be aiming for a warmer sound, rather than just projecting the "melody" note.
(In the Schumann G minor sonata, the crossed thumbs position means that the B flat will naturally sound a bit louder than it otherwise would. It also has the nice side effect of putting the left hand in the correct position for the following bar. And the jump is the same sort of gesture as at the start of the Hammerklavier,
albeit on a much smaller scale.)
3. Sometimes composers do illogical or unnecessary things just because it feels good! A cute example is Bach's prelude in B flat from book 2 of the WTC. There are plenty of passages where one hand jumps over the other. Typically the left hand will jump over the right twice, then right over left twice. He could have just had the left hand jump over every time, and it would have sounded just the same and perhaps been a little easier to play, but I guess it pleased him to make it more symmetrical.
On the whole I tend to take a pragmatic approach. It's good to speculate about why the composer might have written it that particular way--great composers usually have reasons for their decisions, they are rarely careless about these things. So you want to have a clear idea of what effect you're trying to achieve. But then it's up to each pianist to find their own way of achieving that effect. And if rearranging the notes gives a better result for your hand shape, there's no harm in it.
(The argument "if it didn't make a difference Schumann whould not have written it that way" on its own doesn't wash with me. You need to know why
it makes a difference, otherwise the whole exercise is meaningless.)