I agree. When I hear "az asztal mellett írok" I imagine myself sitting beside the desk, with a clipboard on my knees and writing like crazy.
Imho the correct version would be "az asztalnál írok", likewise in English "I am writing at the table/desk".
"i" is a funny vowel - it used to be two - a front one and a back one. Now it is not clear from spelling which it is/was. It is usually front but quite often back. You just have to memorize which is which.