The rationale for BA's free seat selection structure has been endlessly discussed on FT so I won't rehearse the pros and cons. It suits a lot of customers and not others.
People who aren't eligible for free seat selection have a choice. If having a particular seat is important to you, it can be guaranteed by paying the fee. if it's not that critical, you can choose from what's available at check-in. Your reluctance to pay outweighed your preference for particular seats and unfortunately it turns out you made a bad judgement call on that. Perhaps not surprising given that the WT+ cabin is so small.
Given where you are now, I would still check in online at T-24 rather than leaving it to the airport. Other seats may have been freed up.
re. EDI-LHR. If your onward flight is in WT+, as you seem to be saying, then that's not eligible for business check-in, lounges etc.