This does not answer the question: Will BA force me to pay for advanced seat selection regardless of the class? Economy class tickets (basic or main cabin) require payment for seat selection, right?
It will not force you to pay for seat selection.
If you have no status, then there is a charge if you wish to select seats in advance of check in
If you have Oneworld Ruby status (AA Gold) , then you can select for free from 7 days prior to departure
With higher status, you can select once ticket is issued