Upgrading Skill Gems

Is there any purpose to upgrading your skill gem versus just unequipping the one you are going upgrade in order to craft a brand new, higher level skill gem while keeping the old one? Is that something that can be exploited for other characters?

If so, players should be rewarded for upgrading a skill gem, besides just levels. Maybe you can incentive the use of one specific skill gem by giving it a quality upgrade when you get enough experience with it, up to maybe 5%? Or maybe we get currency rewards for using the same skill gem for a long time?

the reason to upgrade is because the upgraded version will keep any sockets and quality that it had before, not relevant early game unless you use currency from a previous character, but important later