One reason people stand on the side is to avoid turning one’s back on the Sefer Torah – which is often being held by the one who did Hagbah directly behind the Bima, in such a way that if one stood at the center of the Bima, he would have his back direcly opposite teh Sefer Torah. By standing on the side of the Bima, this possible lack of Kavod for a Sefer Torah is avoided.
I’ve been in Shuls where, after the Sefer Torah is wrapped, they put it back on the Bima specifically to avoid this issue. They use a Klaf for the Haftara, and the Ba’al Koreh does stand in the front of the Bima (though not in the middle – the Sefer Torah takes up some space) when he Leins the Haftara. When there were three Sifrei Torah used on a Shabbos, and there was not enough space on the Bima for all three and the Klaf, they had someone sit with the third sefer, and the Ba’al Koreh moved to the side of the Bima to lein so as not to turn his back on any of the Sifrei Torah.
an Israeli Yid