Finally found the reason I've never actually played with Parliamentary System: It requires democracy. So it's mutually exclusive with Authoritarianism and it locks you out of agendas. Considering the other options this makes it an easy downvote.
For mechanist... I'm not actually sure if mining guilds or mechanist is better. So I'm voting mechanist, it's certainly very good.
Democracy is the best government type at the beginning of the game, with egalitarians being a more easy than most faction to please, and especially with parliamentary system, you could out-influence any other build, which with one of the other two civics on the list, let you snowball further than the other two combined. (or basically any other civic other than maybe IP)
And unlike mechanist, parliamentary system remains useful later in the game, if you're willing to continue dealing without agendas.
Mining guilds was great regardless... but I don't like it because of just how it was too good regardless what the situation was, and it had no RP potential. It also could be argued to be worse early game versus a mechanist-parliamentary civic combo in snowball potential, though mid-game and later mining guilds would best be used to replace one of the other two...
Which it's easier to get those 250 influence points floating around if you have Parliamentary system.
Mechanist 41
Mining Guilds 49 (-2)
Parliamentary System 20 (+1)