"died into?"
Refer back to Adam's response. There are structural design differences between rimless tanks and rimmed tanks. The trim serves a purpose, to support the tank. It's function may not be obvious, but that doesn't negate it. Ugly trim that is intact is still serving it's purpose. Pretty trim that is broken is not. Any trim that is removed is not.
You can paint the trim, cover it, etc, but do not remove it.