Swapping out the line card involves a different team and a small amount of downtime for everyone attached to the line card. I'm not saying they don't do so. I guess it will depend on how service impacting it is for those on the particular card. BS may know more about trying to push for a line card swap out.
Generally, the process for a faulty port (lift & shift) would be to liaise with the helpdesk advisor, in order for them to test the spare ports available in the Cab, to see if a L&S would cure the customers issue.
Hard to put a nationwide percentage on it, but experience would tell me this is successful 80-90% of the time.
From time-to-time though, as part of this liaising procedure, it will be found that any number of the spare ports that exist also have faulty issues. The advisor has full access to the full cards performance and will scrutinise said card before making their next decision. It may simply require a full-card reset, but these things aren't done lightly for the obvious reason.
The advisor also has the ability to mark any spare ports as 'faulty', which can then 'force' the system into looking for a spare port on another card ... but only if one is available. If the Cab is at capacity, then there is nowhere left to go other than to raise a 'LLUMS Case' for one of the other BT departments (I forget now, BT Operate or something like that ??) to carry out a card change.
I can't comment on the turn-round time on these, at it is varied. Can you speed the process up ?? Not a cat in hell's chance, I'm afraid.