When an empire has both >100 worlds and >2 sector capitals, sector capital secession becomes a major risk. The L&O doctrine has a mechanism for preventing secession (a base secession adjustment plus imperial guards); other doctrines do not and empires using them will inevitably undergo a secession event once they pass the threshold (it's possible that this can be staved off for a while by abducting imperial guards from other players, but this is not a viable long-term strategy)
Planet density seems to be adjustable during game creation, since different planet densities and clustering were seen in different Alphas and Betas. In Beta II, it's possible to build an empire with considerably more than 100 planets in a 2-sector-capital zone (case in point: University, which has a stable 156 planets under F&M).
On a less dense map, non-L&O doctrines will be less competitive outside of the very early game because the total number of planets that can be controlled by two sector capitals is lower.
Another example: on a hypothetical small map with only a couple hundred planets there would be little to no incentive to adopt L&O except for a player who has already effectively won the game by controlling the majority of worlds.
To make doctrines more consistent across different map types (if secession is retained as a mechanic) I suggest:
a) remove the sector capital count risk from all doctrines and have it solely be a function of planet count or net population.
b) make the planet count at which secession becomes a risk be a function of map size and possibly total planet count, rather than a fixed number. Have the secession risk threshold be prominently displayed in the doctrines tab.
c) make the total number of allowable sector capitals a function of total planets in the empire, so that players can't use the sector capital spam exploit, but also link this number to map size and planet count. Allow players at least 1 freebie sector capital establishment regardless of empire size but do not allow establishment of additional new sector capitals if there are less than a certain number of planets in the empire, and increase secession risk if there are more sector capitals than allowed based on planet count (this will allow empires to organically collapse during war even if their sector capitals are unassailable- whittling away at resource planets will cause secessions after a while).
d) Secession should use civil war mechanics rather than occurring instantaneously, so that players can head it off by force if they want to keep their preferred doctrine. Whenever a secession would be triggered under the current system, a larger-than-normal civil war should start on the sector capital that would have seceded. Any time a sector capital goes independent through civil war (regardless of how the war started: shortages or secession trigger), the result should be a secession empire.
e) Crushing a secession-triggered civil war should temporarily decrease secession risk.
e) There should be no social order penalty for retaking planets from an empire that seceded from yours, and retaking the capital of the secession empire should bring back all the planets that seceded with it with no efficiency penalty on those worlds. Retaking secession empires should temporarily decrease secession risk. Social order penalties should be as normal for empires trying to attack empires that seceded from other players.