No, I don't think "max" ranks is the real issue here. The problem is once AD&D became a skill inclusive system, it bombed the whole concept for starting characters. Using a flat D20 means needing THE ABILITY to get a starting character to about +10, +11 with stat mods for a class skill. If it's a fighter, that means HAVING the skill points, and not being restricted to level plus 3.
Strength 16, max ranks in Str skills is 5, +1 for lvl, +3 for stat mod = +9. Much better. You have used 5 of 16 Str skill points to be a decent swimmer at start. You still have 11 points to spend on Str related skills.