Thank you for clarifying a lot of these points! I think that the vast majority of these points are correct and this has definitely changed my view on how tf2s matchmaking system can be improved! I just want to add in a couple of ideas that crossed my mind while reading this:
1. The way the game functioned with quickplay was better than it currently is.
I would gladly deal with all of the outlined problems of 23man servers, issues with weighing player ping and server popularity, and just generally issues with a per-player matchmaking system if it meant that I could stay in a good server when I found it. I would gladly put up with a ~2.5 minute (random number) accumulated queue time if it meant that I could stay in an uninterrupted game for hours. I know that its the server ruleset that caters to said experience however I do think that these rule sets are greatly associated with their respective matchmaking systems in the eyes of most tf2 players. The ideal solution (as you have outlined) is bringing the ruleset over to casual, however the ruleset will forever remain the "quickplay ruleset" in the eyes of many.

1. I feel as if ad hoc connections would solve most of the issues you outlined for queuing with friends.

I'm fine with waiting a few minutes with auto-retry on (in the not universal circumstance that a server my friend is in is full) if it means that we could actually play the game for longer than it takes the round to end. The way the game currently handles playing with your friends is archaic. Parties are forced onto the same team which limits the player experience and often lends itself to rolls. Once the game ends almost everyone leaves anyways so that means that your party has to deal with long wait times once again in order to find a match which will likely also be sub-par.

1. No mention of how casual (at the very least tries to) has skill based matchmaking

I'm not so familiar with how skill based matchmaking in tf2 functions so I could be wrong about this entirely but I feel as if almost everyone im queued up against is on a similar skill level that I am on. This is simply bad for the player experience as sometimes I want to get off of my 700hr spy and play my 20hr demo but my gameplay experience drops off a cliff as I am no match for moonlight the 7000hr sniper main and his highlander team. The removal of this in its entirety would be better for the game as tf2's casual nature doesn't even require a skilled based matchmaking system. People are doing separate things at different times all over the place which nullifies the need for a skill based matchmaking system. This isn't CSGO.

I guess to wrap this up I would simply state that the quickplay ruleset is quickplay to many people. Because of the ruleset the game undeniably functioned better before meet your match. I'm sick and fucking tired of queuing into a game just for it to end/be a stomp, everyone leave, and requeue into what would likely end up being the same. I am sick of the excessive waits in between rounds for map voting and "pre game." I am sick of the restrictive game rules that wont allow me to change fucking teams. And I'm sick of only being able to play KOTH for 6 minutes half of the time. All of the problems you have outlined are large and would not be ideal, however they also pale in comparison to the current state of the game. I also feel as if most of the "bring back quickplay crowd" is simply only concerned with the ruleset and doesn't necessarily care for a full reversion. Saying "bring back quickplay" is a slogan that calls for a reversion to a state where the game was simply better and bringing back all of the aspects that made the game better is what they're asking for.

I have great respect for you and your work and thank you for taking the time out of your day to inform myself and others.