Hi yes you are right in that when you raise the front sprocket by one tooth it is equivalent to running the lower sprocket with around 6-7 teeth more. You can punch in google kart gearing sprocket calculator and charts will come up showing what is equivalent to what. Once the gear ratio is equivalent then there really isn’t any performance benefit to running one over than the other…the benefit might be more a clearance of rear sprocket to track thing (the smaller rear will give more clearance for curbs etc).
As for you question on if you ever need to change, the short answer is yes. It is all dependent on the track, chassis setup, engine limiter and much more. The shorter you go on the gearing (going bigger with the sprocket axle and leaving the engine sprocket unchanged or going down on the engine sprocket and leaving the axle sprocket unchanged) you will gain acceleration potential but at the expense of top speed. The converse is true if you do the opposite. How do you know which you need to be on? You gotta test it but gearing is something that is also driver dependent. What i mean is, the best drivers will always be geared longer than novice drivers, meaning they can still roll the same or more speed than the novice guys in the slow bits but then get a huge advantage in straightline speed vs the shorter geared guys. This is where chassis setup comes in as well. If you dial the kart in to roll through the tight stuff really good, you can go longer on the gearing and gain straightline speed potential. Hope I didn’t confuse you too much