Disclaimer : I have not played the game since I completed the restoration campaign right after launch. Nor am I an expert on Battletech lore. Please excuse if some of these are already patched in / planned, or are counter to the Battletech universe (though I do believe some concessions can be made to lore designed for pen and paper for the sake of a good computer game).
The issue with the sandbox gameplay in Battletech is that it is pointless. My actions have no effect on the world. Systems do not change hands. There is no way to strategically affect the economy etc. It is a pointless repetitive grind. You have mentioned Sid Meyer's Pirates. You should borrow some ideas from them, and other similar games like StarSector, Mount & Blade etc. It should have features like -
1. Factions should be dynamic. They should have roving fleets / armies that it can send out to patrol or against it's enemies. They can make war, sue for peace, and all that.
2. There should be other persistent autonomous mercenary fleets that the player needs to contend with.
3. The player should be able to escort, intercept / fight and interact with these fleets, trade equipment or fight beside them for a price etc.
4. There should be other travelling fleets (merchants etc) that player should be able to attack for resources, causing penalties with their parent factions.
5. There should be tactical missions available in systems such as destroying industry, arms reserves etc that can affect the state of that system, such as availability and prices of equipment.
6. Contested systems can have a balance of power between the contending factions. Completing enough missions (both by player and other forces) should make the system change hands.
7. There can be dynamic missions created based on the state of the world. For instances a system facing a scarcity of food may provide a high paying mission to escort a relief fleet send from a different system.
8. There can be famous mechwarriors - mercenary captains or faction members, that you can defeat to get special equipment / mechs or recruit them to your fleet.
Edit : I just remembered I posted something similar in suggestions a long time back, lol.
https://forum.paradoxplaza.com/forum/index.php?threads/dynamic-open-world.1096109/#post-24201959