Required may not be the best word. Nobody needs to do anything. If the developers desired, they could have left Battletech's setting stuck in 3025 forever.
A better question is: Would such changes benefit or detract from the board game?
So going down your list...
- Allowing more existing technologies
Existing technologies include weight-saving items such as endo-steel, ferro-fibrous (or other specialty armors), and other fancy stuff.
Such technologies were banned from LAMs, presumably so they wouldn't be too effective. That's a perfectly reasonable concern to have, even if I disagree with it (I've experimented with much of these in an AU setting). Whether lifting those bans would impact tabletop balance too much is largely a matter of opinion, and it can be successfully argued either way.
Other items, such as Omni-technology, are also prohibited, despite not having any actual impact in a pick-up game. Precisely what would have been lost if the Spectral LAM series had actual omni-technology? Another restriction is that LAMs cannot be built as a quad or a tripod, the reason for which is lost on me. Is the Scorpion LAM going to dominate the battlefield in ways the Phoenix Hawk LAM could not if it could take off the ground without ripping itself apart? No.
Yeah, having those prohibitions don't really help anyone but the ink & logging industries. The more pointless red tape that gets axed from the rules, the better.
- More new technologies
Question: By more new technologies, are you referring to a general technology that might be added in the future (For instance, a "Autocannon Mk.2"), or technologies that are specific to LAMs? And in either case, could you give some examples of what you'd have in mind?
- Heavier LAMs (Heavy or Assault class)
Yeah, that one easily falls under the "red tape" I mentioned earlier. The Champion LAMs and other potential heavy LAMs will inherently be on the slow side on the Aerospace scale for obvious reasons. If they don't get produced, it should because they're not effective in-universe and not because a some random rule decrees it. Cut the tape.