It really depends on the tank, and the thickness of the glass. If the trim includes a plastic cross brace it isn't a good idea. These days, glass thickness is at an absolute minimum, to keep costs low. The cross brace makes up for the deficiency. There are still tanks being made with glass thick enough to not require cross bracing. The local Big Al's has a bunch of 120s with no center brace. These are 6' tanks, about 22" tall, and the trim is add on type cut to size to fit and cover the top edge. It doesn't really add any support.
If you are having an issue with broken cross brace, the bottom trim can be swapped for the top since they usually have a cross brace they don't need.
Join a fish club. Don't have one in your area? Start one.