I was thinking the same, one way might be just to simplify the system at hand.
Lets suppose we have a ranking system where by your default rank is 10kyu. Now theres two settings for simplicity B and L (live and blitz, why not) and and overall rank O, all computed separately from each other. Only one board size allowed for simplicity like 19x19.
Here’s the simplified rules:
- You can only play even games (eg 6.5 komi japanese, or your favorite ruleset)
- If you win a game against an opponent who has the same rank, or a 1 rank difference, your rank increases by 1, if you lose it decreases by 1.
- if you win a game against a player of 2 or more ranks stronger, your rank goes up by 2 and if you lose against a player of 2 or more ranks weaker it goes down by 2.
- If you win against a player 2 or more weaker you don’t change, or lose to a player 2 or more ranks stronger, no change.
- To update the ranks of B, L and O you only compare like ranks.
So you start off playing lots of L games, eg lets say we could say you win 5 even games and go up to 5 kyu, then you lose two even to 7kyu, and win against a 5 kyu so back up to 5kyu. All these games used your O rank when pairing players (imagine an automatch).
Where did/can your L rating end up?
- If everyone you played had matching L and O ratings, then your L and O rating should match at the end at 5kyu in this funny system.
- If however one of your opponets L and O rating differed, eg in the last game (you O-7kyu L-7kyu, opponent O-5kyu L-6kyu) now what? Well the O calc is the same, you got to 5kyu but your L calc bumps you only to 6kyu.
This shows that any imbalance on one player can propagate to other players
In the second case we can already see that the average doesn’t really match (B+L)/2=(10+6)/2=8kyu whereas O=5 and L=6kyu. Maybe there is some funky average that makes it work, but at the moment B is static while you play L games, and O and L can change separately so it seems unlikely that the weights would be fixed to always make the average work out (maybe it does?).
Now lets mix a Blitz into it. You now decide to play 5 Blitz games to get a Blitz rating, all against even opponents. You win 4 and lose 1, how do your ratings look? (there’s loads of ways this can go)
- Imagine automatch and it pairs you by O ratings: You win 4 and you’re bumped from O=5 to O=1 and then lose and back to O=2, L=6 still.
- If your opponents had matching B and O then you go from B=10,8,6,4,2 as your O=5,4,3,2,1.
- many other variations
Actually even at this point (before the loss) you can see that O=1 B=2 and L=6, so O>B,L.
It looks like O>B,L in simple examples
I think it just being possible in a simple system, I’m happy with, so I’m cutting off my analysis for now 
I’m trying to see if I can make a simpler version, but something not too dissimilar from ELO or GLICKO.
- The idea that you gain more when beating someone much higher rated, lose more when losing to someone much lower rated.
- The idea that losing to someone much stronger doesn’t really matter, and beating someone much weaker doesn’t really matter.
I was imagining somekind of cutoff/steps in the rating (in this case ranking), rather than the continuous ELO/Glicko ratings.
Feel free to pick apart the above examples, I’m just kind of throwing it out there on the fly 