Firstly, a balanced rig does NOT preclude ditchable weight. It simply considers what that weight might be... not just lead. But every diver needs the capacity to:
1. Ensure positive buoyancy on the surface.
2. Ensure they can rise in the water column, even if unable to inflate/retain gas in the BCD.
A ditchable weight belt is the simplest solution to achieving those aims - and that simplicity makes it the chosen method for entry-level scuba training in most agencies.
The debate regarding risks of accidentally dropping weights versus not having timely access to positive buoyancy is primarily a matter for technical divers. Accidentally losing weight, and resulting uncontrolled rapid ascent, is likely to kill a technical diver. An open water level diver, diving conservatively as advised, isn't anywhere nearly as inert gas saturated.... so DCI is unlikely... and easily resolved if it occurs. Fatality is improbable, except if they held their breath... and that's a skill/training issue, not an equipment one... As others have said/will say, you can fix bent, but you can't fix dead.
Far too many divers drown having already reached the surface and, failing to quickly achieve positive buoyancy, sinking back down. For that reason, the diver must be able to ditch weight. The weight belt or quick-release pockets etc, is the most straight-forward method of doing that. Technical divers, in balanced rig, have other stuff to dump... deco cylinders, canister lights etc etc... and they (should) have the training, stress control and presence of mind to achieve that if needed. Such assumptions cannot be made about recreational divers as a whole...
What is missing from basic scuba education is the concept that the diver ONLY needs to dump sufficient weight as to achieve positive buoyancy. That needn't be ALL of their weight. 1lb positive is still positive. The only way you will go is UP...