It was a strange feeling being involed in the early matchmaking beta. At first, Valve seemed to be working based on the feedback that was given by the beta-players (mostly top-level players) by listening through players' streams, but as time went on there were less and less updates to the system, even though it had some pretty big structural flaws. Suddenly, the matchmaking system was released to the public, without any big improvements to the system. I suspect this release was done because players gradually stopped beta-testing. But on the other hand the beta-testing had already been done and people were waiting for the feedback to be implemented. Of course, having no direct communication between the players and the developers makes this a lot harder to communicate.
One of the reasons why matchmaking failed is because it restricted a lot of settings and forced players on higher quality settings. It was theorised back then that having players stream on higher quality settings would make competitive TF2 more watchable, and bring in more viewers. But on the other hand, playing TF2 with high settings causes a lot of FPS issues on older hardware, and generally having the game look nicer can negatively affect gameplay. So there are pros and cons to this, but it seems that a lot of players weren't willing to migrate to matchmaking and this was one of the reasons.
Another reason was the ruleset. Valve did not like any of the competitive rulesets, so they had their own version, simply a best of three on 5cp maps. I have no idea why this ruleset was implemented, it doesn't seem like removing the timer would solve stalemates (assuming they would even happen that much in a matchmaking environment), but it also made games either really short or really long. A game could be 3 minutes or 40 minutes long with that ruleset. Also, since most of the playerbase was already playing their own ruleset, playing matchmaking with a completely different ruleset and no whitelist was simply not worth it because of how different it was.
Soon after the release of matchmaking, it was apparently riddled with cheaters. TF2 didn't have the overwatch tool that CS:GO had to weed out the most blatant hackers. So these people could cheat mostly without consequences, which obviously completely destroys people's experiences. I think this was the biggest factor why it flawed even with the public players who didn't previously play competitively.
It's not a pretty story. It shows how difficult it really is to create a matchmaking system, especially in the environment TF2 had. I think matchmaking could have been successful in TF2, but I think it would have required more open-mindedness and communication from Valve in the early phases in beta testing. I don't want to be overly critical of Valve because the situation was difficult to begin with, so I guess my attitude is, "at least they tried".
Apologies if I got some things wrong, this was three years ago so I don't remember things exactly how they were.