You could get a scan but if you are easily and recurrently spraining then perhaps you have a complete rupture of the ligaments. No amount of rehab will replace that although bracing and/or strapping is a useful preventative method. I would prefer a strapping approach to football myself. This is common and somewhat effective.

The issue is like that with the any ligament (e.g. ACL) in that the ligaments provide a direct feed forward path to the brain about what is happening at the ankle e.g. hey brain i am rapidly rolling over. The brain say (hopefully quickly) 'OK well best I tell the muscles that stabilize the ankle to stop that from happening.' There's a few other receptors but the ankle ligaments are very impt in this pathway.

Now if you rupture them completely there's no early warning sign to the brain so by the time the other receptors work it out it's already to late for the ankle! Surgery will not replace that early warning sign. It may of course give you some local stability to give you more time for other receptors to kick in. If there's not a complete rupture and the ligaments are stretched then as there is a length tension relationship to the recptor simulus then it takes more stretch (therefore more time) to get to the desired level to let the brain know. This latency can mean you're already over on your ankle before the brain gets the warning. Now this is where most of the rehab is aimed. Resetting the brains response to other stimuli, joint receptors, tendon receptors in the peroneals. Taping to provide further feedback to the brain will help.

I hope this gives you some insights into the issues and provides more questions to ask of your physio and surgeon.