My question is: Suppose A gets the login id and password of B which has higher authority than A, that would compromise authorisation because once A gets falsely authenticated as B, A gets all the access privileges of B.
Not necessarily. Authorization can be tied into any number of things. For example, User B may get different authorization profiles based on the type of device (computer vs. mobile device). Or they may have different profiles depending on the how they are connected to the network (wired vs. wireless vs. VPN, corporate headquarters vs. branch office, etc). Or, as a final example, the date/time may determine what authorization profile is applied to the user.
So just because User A can use User B's credentials, doesn't necessarily mean they will get the same privileges.
So what is the whole point of authorisation?
It allows you to centrally administer what a user/device can do depending on a wide number of factors. It allows you to consistently and more reliably apply privileges to users.
Say an employee's job responsibilities change (they get promoted, position gets modified, etc) and you need to adjust privileges. You could do so by "touching" each resource they need to have their privileges changed. Or if all those resources were using a central AAA server, simply changing the privileges centrally will grant them those privileges quickly and easily (and less prone to missing resources or human error when making repetitive changes). Often this is as easy as changing/adding a group membership to their user account.
Or say you have several employees that should have the same privileges. They can all share the same authorization profile. Again, simpler to manage and make sure that their experiences are all consistent.
Is it dependent or independent of authentication?
In some senses, both. Authorization takes place after authentication, so on the one hand it doesn't take place until authentication takes place (even if it is an "open authentication").
On the other hand, authorization is an entirely separate process than authentication. The authentication may or may not determine what authorization profile is applied.