Sorry to be the dissenting vote here, but from a structural perspective, the rims are much more than purely cosmetic and definitely add strength to the tank, of whatever size- as long as the frame is one-peice, molded. As already stated, especially with a center brace. Because it is siliconed in place, it supports the panes from the top, like the molding around the bottom, from pushing out. Without it, water pressure pushing on the top of the glass pane would have far less resistence- with only the corner seals holding it in place. I'm not arguing whether or not a tank with it removed will collapse or not, time would tell, but it definitely adds rigidity in all four directions. I wouldn't remove it. If you want to add a glass brace after removing it, it would have to be in both directions if the aim was to replace the frame's stabilizing function.
I would posit that taller tanks would fair worse with a removed trim than shallower ones.
