Whether you do so or not depends heavily on the sort of diving you do.
If a diver has a problem while recreational diving, they are free to surface to respond to the problem. In such cases it might be prudent to have some ditchable weight.
If a diver has a problem while technical diving, this is not an option. Technical diving might be defined as 'diving in which surfacing to deal with problems is not an option'.
This is because there is an overhead, either tangible or intangible.
A tangible overhead is an obstruction that prevents one from surfacing. This could be, for example, because the diver is inside a cave or a wreck.
An intangible overhead is a decompression obligation that might put the diver in a wheelchair or kill them if they surface, whether they technically could reach the surface or not.
Therefore, in technical diving surfacing to resolve problems that occur underwater is not an option.
Being able to drop weight in order to facilitate surfacing becomes, therefore, irrelevant.
In technical diving the objective is to prevent the problem before it occurs by ensuring it does not have a chance to occur in the first place. Alternately, one is prepared to deal with the problem while submerged. Recognizing that one absolutely can not surface to solve problems brings a fresh clarity to one's perspective.
Diver's who cannot ditch weight to surface need not concern themselves with whether their weight is ditchable. They DO need to ensure, however, that they are properly trimmed and are able to hold decompression stops under nearly any condition. That is not always as easy to achieve as it sounds, and this is why technical divers may use trim weights such as V-weights or P-weights on their rigs.