Barriers are not very comprehensively programmed to determine which tickets they do and don't accept. Just because a ticket works the barrier, that does not necessarily mean it is valid - and vice versa, rejected tickets can be valid too.
London Thameslink is a fares destination which includes all of the stations between London Bridge/Elephant & Castle and St Pancras. It does not include all of the traditional London Terminals such as Victoria, Waterloo etc.
You can still travel to any other London Terminals that are on a permitted route to somewhere like London Bridge. Historically speaking this would have permitted travel at least as far as Clapham Junction on the way to Waterloo, where you could change for Waterloo East and then London Bridge.
However,
@miklcct 's insistence on raising this to the TOCs' attention (despite being warned of the likely consequences) resulted in a
negative easement being created, which now bars such routes:
Therefore you can't travel to Victoria on such a ticket and would need another ticket from Balham to cover your journey into Victoria. Since you have a season ticket, the train doesn't need to stop at Balham for you to extend your journey to Victoria with an additional ticket.
However you would need to buy the additional ticket (e.g. as an eTicket) before the train departs the last station where your season ticket is valid - i.e. likely East Croydon if it's a fast service. You can't just touch out at Victoria with an Oyster card or contactless card/device as you need to touch in
and out to validly make a PAYG journey.