I have figured out why the Initrd image needs to be regenerated(to add the modprobe blocklist configuration file to the initrd so that the conflicting modules are not loaded and only then the 'wl' module can be loaded correctly. In my case the ssb module was loaded when the blocklist config was not added making the 'wl' module unloadable.).
But now as REMAKE_INITRD is deprecated there should be some other method for automatically regenerating the initrd after installing broadcom-sta-dkms package or atleast the Debian wiki should be updated with the additional note of manually regenerating the initrd after installing the package.