Your calculation is missing that happiness is capped at 100. So even when "your Average X is >0" Allegiance will always stay below 100 (Allegiance can only reach 100 when all your planets have X>0).
What i expect for "normal" empires is that the Allegiance of their starting and native species will settle in the range of 80-95. My goal was not to pester the player with keeping its own folk happy (unless he picks up some difficult species like xenophobics), but to make invasions come at a bigger cost.
I think you are right in that the drift of allegiance will stop because happiness is capped at both ends, but is the feedback loop still desirable? It means that when "average X>0", they will both grow until some planet or planets has 100 and even worse, when "average X<0", they will stop dropping only when some planet(s) reaches happiness = 0.
Think about an empire where some species lives only on one planet. Say the total effect of other factors on that planet is -10. Then happiness will be below allegiance and allegiance will fall, which will make happiness fall, etc... until they rebel. The feedback loop won't weaken before the happiness is capped.
I think I can see a reason for doing that though....
The idea is you have to Control the other factors
It does make it simple in terms of game results... 2 possible results (technically 3 but practically 2)
1. Happiness rises until it is at 100 on some planets (and near 100 on others)
2. Happiness falls until is is at 0 on some planers (and near 0 on others)
Basically there is a Threshold.... regarding the 'other factors'
Above 0 you will win that species over
Below 0 you will lose that species to rebellion*
A simple change for "Target Approval" make it (5 + H1*P1 +H2*P2 ...)/(0.1 +P1+P2...)
That way if you have 0 pop in your empire, it balances out at 50... but if you have 1 pop in your empire, that out weighs the 50 by a factor of 10 to 1)
*actually you will lose the worlds that give the species unhappiness factors first.... so if some worlds have 'other factors' >0.. they won't revolt.. and once you lose the 'poor' worlds... your happiness for that species will rise again.
OK I like it
The positive feedback acts as a switch.. world is stable or not
also if your worlds are highly unequal...
1 Paradise homeworld (+70) and 5 poor worlds (-10 each) [that somehow have the same pop to make this balance]
The Paradise world would be at 100 happiness, the Poor worlds would all be 10 below the average..
So the poor worlds would be at only 40 happiness
...or of they have 1/5 the pop of the paradise hw (more likely)
poor worlds at 80
So while overall it tends to 'go up v. go down'.. there will be a few worlds that have stable but low happiness (so they can be vulnerable to spies, etc.)