Isn't it just that you cannot change your seat without a fee and you get whatever BA assigns you?

What I mean is, at the time of booking you have the option of paying a seat selection fee and if you don't, you can wait until a week before or at check-in (depending on fare or status) to select or change a seat that has been assigned by BA.

Thus, OP will have a seat whether or not he selects one anyway?