I have to disagree on the notion of characters having every chance to find a god just by tagging out. From personal experience, I've had Dust and Nia in game for a long time, and yet when I went looking for gods, got barely any takers. That's with all that in-game experience behind them, and knowing and interacting with many people. New characters are going to have even more of a disadvantage if the players don't know someone in-game.

As for "obscure and unpleasant characters are unavoidably handicapped", I disagree that it can't be ameliorated on the basis that random assignments DID ameliorate it. Which is one of the reasons I apped a character who would otherwise never voluntarily look for the CR I want him to get from a shinki. That was a selling point for the game, and I think it remains so -- making it necessary by nature for characters to team up and interact with each other is a great way to branch out. Honestly, I've really felt the loss of having a shinki character with Zetta over the past few months, and I'm really not comfortable with being told I will, basically, never get one again. That straight up isn't what I signed up for in this game.

And that still doesn't address the rich-get-richer nature of the new 'only choose your pairing', especially if people can coordinate ahead of time with the host god's player to
have them encourage this or that pairing. This will make the game more insular and freeze out more people, rather than encouraging greater CR and greater connections among players.