I'm not a big fan of the "you always have to wear this brace due to this injury" mind frame. Of course there are exceptions to the rule, but overall I think proper rehab can overcome most laxity issues. How did you originally injury your ankle(s)? Multiple occurrences of ankle injuries? Do you generally have laxity throughout all of your joints?
By addressing and correcting your ankle proprioception, strengthening and mobility you should be able to restore normal function to that ankle. To answer your last question, having a deficit at your ankle could lead to knee problems down the road depending on how the forces translate up the chain. If you lack dorsiflexion, you will most likely place more anterior shearing force on your knees during squatting based movements. If you over-pronate your foot, you can lead to a knee valgum position and cause stress on the medial structures of the knee.
Basically, having a deficit, whether strength or mobility based, at any joint can cause issues for joints further up or down the chain.