You are right, but writing or even using a regular computer mouse requires the use of more proximal muscles, not only the distal ones.

In order to write you have to keep your arm above the paper, you also need to move your hand from one side of the paper to the other. for this you need to use the muscles of your forearm or even your shoulders. We normally don't notice having to use those muscles because they are much stronger than what is required for this task.

The effort of writing also depends on the pen you use and the way the weight is balanced between its top and bottom. Some pens are much heavier on the top and then you have to resist their pull down. Others are relatively heavy and require more force to be moved as you write.

Try this: rest your arm so it is fully supported on the table and then only move your finger tips or the palm of your hand.

Now do the same, but this time slowly move your hand from side to side.

Now try to do the same thing while holding your arm slightly above the table.

I can easily type with my arms fully supported and use a laptop or trackball mouse. But, I can't use a regular mouse or a less soft keyboard for more than a few moments.

I can only write with cheap light-weight pens. (which is an economic advantage )