The original military Jeep is a pretty good analogy of how the BT universe operates. The US had the Jeep manufactured by several different companies, since the original manufacturer could no longer keep up with demand. It was made a criminal offense to modify the design without approval, since supplying different parts for different versions would have been a logistical nightmare, and virtually all of the approved "upgrades" to the design were directly interchangeable with the original components or sub-assemblies. It wasn't until post-war and the revocation of the restrictions that variations and changes were made, yet the basic design still remained mostly untouched for a few more decades (completely new designs were introduced, but did not REPLACE the original), and remained fairly static until the company was bought and sold a few times.
In the BT universe, with the difficulties and costs inherent in shipping spare parts for literally hundreds of different designs between different star systems, making changes in the design without the express permission of the House they're going to would be economic suicide. There are already too many different manufacturers making too many different designs for most facilities to stock parts for, and adding sub-versions for those would rapidly make repairs and replacements unmanageable. Given a choice between continuing to provide parts for its existing hundreds of Battlemechs of a particular design, or complicating the issue with two different and incompatible sets of components for basically the same chassis, it's no wonder that the House armies refuse the changes and continue to use flawed designs instead of upgrading. Quick and easy fixes are one thing, but if it's not directly compatible, it doesn't get approved without some pressing reason behind it (like a powerful political backer, who probably has other priorities than pure military effectiveness in mind).
We don't use Sherman tanks anymore, but the US Marines continued to use a Sherman-derived design until only a couple of decades ago. Those were based on a set of designs which originated in the 1930s, although its earlier Grant predecessor based on a lot of the same components was essentially replaced by the Sherman. Unlike the Jeep, the Sherman had significant changes and upgrades made, with radically different models, but like the Jeep, most service components continued to be interchangeable within the entire series, so you COULD use parts from a Grant or early WWII Sherman to fix a substantially different Korean War model. There are still Soviet T-34 tanks dating back to the mid-1940s in service in a few countries, although they're practically all gone. That's a design that had significant transmission problems right from the start, yet it's still being kept in service since the origin of the design in the 1930s. Basically, as long as parts are available, they're still being used.
If the parts are still being made 600 years later, and the chassis is structurally sound (thanks to wonder-tech from the 25th Century), it's at least plausible that the designs would still be viable, although few individual machines would be anywhere near that ancient outside of museum pieces.