I agree with you that moving a cell creates a formatting problem. I'm on the fence about Cut.
When you cut the cell, it cuts everything: text, formulas and all the formatting including text size and it reverts back to automatic. It puts the cell back to the default state. Delete does not do this. So, the tool is available to do what you want, it just isn't called Cut.
Moving a cell with Mark to Move followed by Move or by dragging it to somewhere else puts the original cell in the default state. This, I agree, is quirky. In my opinion it should leave the original formatting in the old cell and simply delete the contents like Delete does and also copy that formatting to the destination cell. I do not think it should revert the old cell to a default font and format. That's my opinion, for what it is worth.
Have you submitted this to Apple via Numbers/Provide Numbers Feedback?