The problem with stop playing the characters is that eventually they'll get dropped out of elite due to other players making it in. I've lost Mii Brawler and Mario a few weeks ago from this and my Pikachu is probably on the edge at this point.
The point I was trying to make is that it might actually not work like that. Several unplayed elite characters get to the exact same GSP. Therefore, considering that my GSP for one character is supposed to show my ranking for said character would be pretty far fetch. I would be the exact same rank for Falcon, Link and Inling for example. That does not seem likewise.
GSP would be more of a global ranking system, that would mean that when you're playing Ice climbers, you're still compared to the whole smash player base and not to the Ice climber's mains.
In the same way, never player character have a base-GSP near you're highest one and playing with them will oftenly match you with people also having gsp near your highest one (in my experience) indicating once again that gsp is used to evaluate your smash level and not your Link level. It's basically in the name : global smash power.
I also noticed that since I have 20-ish characters in elite I've been losing way less point. (I can play and lose to the same guy 8 times in a row and still be elite) This could also be seen as an indicator that GSP is globalized and not character dependent (I won't get to 2.5M if 20 of my roster are 3.3M)
I'll link you a video of a guy who got his whole roster to 1 on different account. It basically shows that GSP is not unique (since 2 of his Mario are 1 GSP for example) therefore it's not a ladder between every Mario, less likely (and once again) not character dependent. On the same way, as he got more and more characters to 1GSP, ont took him less and less games to do so (once again, globalized)
Finally, I think the GSP requirement to reach elite is the same for each and every characters, that it is near, if not, the GSP that you're unplayed elite characters get to (extremely close to elitegsp.com's number). It would be very interesting to correalate character's said required gsp difference from the said average gsp required to the number of answer/ character's popularity. Less answers statistically lead to an higher mistake potential and we could expect an higher difference from character gsp requirement to the average requirement. This would plead in favor of globalized gsp.
Hope I was able to express myself clearly and that it could help in the understanding of gsp.