This was a huge debate back in the Entrenchment beta and the Phase Destabilization was the end result that was generally agreed upon. Doesn't have anything to do with Diplomacy.

This can be modded ... in B5 mod a tug ship can be built that can move a starbase (very slowly) to another place.

there are always balancing issues to consider.  In the case of the TEC, the starbase is already potent enough with all it's weapons and the advent seems to use their fighter/bomber bays pretty effectively.  I mostly play TEC, but I think the TEC starbase is way overpowered IMO.  At least against an AI who can't think to do more than send his entire fleet into the BEAM weapons to get shredded.  Aside from using Torpedo Cruisers or a lot of fighters, it's tough to bring down the TEC starbase.  The thing would be unstoppable if you could just fly it towards the torpedo cruisers or the aircraft carriers and wipe them out.  They are only effective because they can stay out of range of the beam weapons.

It would be nice from a "It could make my life a lot easier" standpoint, but the point is well made - it makes you think about where you should place it.  Do you place it between the planet and the primary phase lane for defense?  Do you deploy it near the cluster of structures on an enemy planet to do the most damage?  do you deploy it out of range of the defender's own starbase?  The vasari starbase moves because, IMO, it deals little damage and dies too easily, so the mobility is a bit of a balancing feature.

that will always be the case, though.  There will always need to be a weakness, otherwise the structure/ship would be a "GOD" structure, and human players will always exploit that weakness.