In the expected environment such as large corporations, the desire for an objective (even if bad) metric is driven by the fact because
yes, being unable to put a number on it
does mean you can't tell if you're improving or not - in every case you'll have some people making points why they believe it's improving and other people making points why it's becoming worse, with the arguments mainly driven by politics; in the absence of such numbers, any claims about a suborganization will be even less reliable as bad metrics - bad metrics can be manipulated, but no metrics means that claims can have no relation with reality at all.
And regarding your latter paragraph, the answer to "Should we continue the system?" depends on what alternative systems can plausibly be implemented for making the same decisions. If the current system causes poor decisions, but the alternatives are even worse (or there are better alternatives which we are unable to implement), then we should keep the current system.
Yes, the whole system would work better if people could just agree on what best needs to be done, and which activities are useful for achieving these goals, but often they can't. Metrics are a solution to a particular problem - an environment with limited trust and plenty of subjective politics, where any non-metric system for evaluating success and assigning benefits will be gamed as well. There possibly can be other solutions, but "simply" not having that problem isn't a solution.