SCC, you pose a very interesting question. But, let's not forget that a lot of the mercenary trade really got its start because of Kerensky's departure and the ensuing succession wars. And, let's also not forget the long period of time that those wars were fought over and how a culture can form from repeated processes over time.
People have done a great job covering Neo Feudalism in the light of vast distances and slow communication. Each world is it's own island.
(While I can't back this up with the current 1st and 2nd Succession Wars books, not having read them yet) It seems to me that the mercenary trade didn't really get started until the Succession Wars, or just before, with all those Hegemony and Star League regiments staying behind. The house lords sought to buy these guys out in order to ease whatever Hegemony world-grabs they had planned. A lot of these units would still have a strong Esprit De Corps, wanting to keep together. They're also not stupid, foreseeing that they would be put to use, and would need replacements. They work into their charter a means of acquiring replacements that won't tie them to the state. Desire to own them, combined with no really solid way to hunt them down and eliminate them, (not without unifying the rest of the remaining hegemony forces against said lord) means that the Lord acquiesces. Remember that there's still a significant Hegemony navy, too, not just land forces.
You have the real start of your independent market. But, there's precedent, as well. Let's not forget the bout of ronin duels during the height of the Star League when Kurita warriors would face off against Star League and Hegemony knights. Those guys got their Mechs from somewhere.
So, you have your Star League regiments on retainer with contract that allows for a means of acquiring replacements from the state's manufacturing supply. Then, as the wars rage, and warriors of said mercenary regiment prove themselves and their loyalty and skill above and beyond, nobles and house lords start handing out titles, and the regiment's personnel slowly get spread to the corners of the realm.
But, by the time that a coup might be plausible, you've had the mercenary trade on hand for a long time, a couple decades at least, and local lords and lasses are taking advantage of it during peacetime to get payback or some such. It's also a great means of plausible deniability for the state in general, when they can point the finger at some lower-end schmuck when his raid goes sour or gets traced back to the Realm.
By the time you get to the third succession war, raids are the normal thing. The mercenary market exists, and its much easier to just hire out, leaving the costs of recouping and salvage and what-have-you to the forces on site. After a couple hundred years, it's so ingrained into the fabric of life in Human occupied space that it doesn't go away without a really strong stimulus.
You got to look at this less with modern lenses, like we normally do, and envision that there are a lot of things that become status quo through a process that isn't connected to just any one thing or event. What we accept now as real in the 20th and 21st century on a planet-bound Earth can easily change due to circumstances and necessities when we get to the stars. We've not seen galactic conflict, and we've not seen the defection of a large super-power's military into some nebulous exile where they can't be followed or found, leaving what's left of who stays trying to figure out how to stay alive and not get creamed.
Who knows what will come out of that.
The mercenary trade from the early succession wars probably saw the start and rise of the salvage industry. It really didn't get heavy until people were going back to nuked graveyards to find workable components to keep equipment functioning when the Quartermaster couldn't come through.
And, there's one other aspect that you brought up that is also a big element of BT: Pirates. Lots of people defect from their leige and depart for parts unknown. Many small pirate kingdoms have entire regiments of Mechs that they've stolen or found some other means to make. (Not enough background on this. I wish there was more.) Throw in the fact that house lords and their vassals have been making similar piratical seizures from the enemy for a time, (Hanse Davion made a raid just to acquire some of a certain design) and it really throws a wrench into any idea of security procedures and being able to track down any single machine. (There were over 100,000 Archers produced alone over the course of the succession wars, if you still hold to that tidbit from the original TR 3025. The amount of mechs put out far outstrips the size of the current armies, and arguably the amount of combat losses. Throw in years of frankenmech chop jobs to keep a small handful in outstanding shape, and good luck trying to identify if that belonged to the 34th Red Bull Company, 113th North Continental Regiment, Sudeten Militia when it was 'lost in combat' in 2813 from an exploratory raid by an 'unknown foreign aggressor strongly resembling a Kurita strike force'.)
Aside: The Mechs in question that fall through the fictional gaps, not covered by the field manuals, but strongly hinted at by large numbers of machines have gone somewhere! And, there still aren't enough because you have dispossessed pools of qualified warriors. Combine that with large numbers of mercenary commands that are not accounted for, as well as militias most likely stocked to the level that their planetary governors will allow without becoming potentially belligerent to the higher powers. That looks like there's a large enough surplus for a thriving market that took off at some point in BT's history and never stopped.