The patrician elective succession is lovely. You get to choose your heir with an honorary title. The costs to
rig campaign for the election are usually nominal unless your heir is very young. Though choosing a young heir can be very worthwhile, since otherwise you have the seniority issue of rapid successions due to old age.
Plus losing the election is hardly a disaster. You personally lose out on all the income and levies beyond your personal demesne, but the republic is just as strong. It can be a bit amusing to see what the AI does during its term. Besides which, it's even a bit easier to retake control upon the next election because it's mostly a matter of prestige. Since your family should have the largest demesne, you can just join or declare wars and probably gain prestige much faster than any other candidate. (or if you're a pagan, raid for insane prestige+loot). And even though I usually avoid murder unless a character specifically wrongs me, plots against the current Doge seemed to attract plenty of plotters.
The levies do seem much lower than in a feudal state, probably because the main vassals (the other patricians) use the mayor laws for taxes and levies. And you can't increase crown authority past... limited? The second lowest.
But on the flipside, they use the mayor laws for taxes! Minus 50% but still. As Doge of an established trade republic you'll be making mad money. This is one of the few times when being a pagan sucks... My Principality of Mali only ever had one mercenary group available. Though the Spirit Guardians holy order were a nice bonus, particularly once vassalized. In my run as... Genoa...? I remember that the many mercenary groups of Europe essentially *were* my army. I was making *that* much money. Along with retinues, which are (despite nerfs) still incredibly powerful.
My Italian run eventually ended due to running out of male dynasty members somehow, which took me by surprise. My Mali game has no dangerous of that, due to concubines.
EDIT: Oh right, also you can invest some of that mad money into your pocket dimension, the manor. The upgrades are expensive, but pay off... By the end there are substantial stat boosts, and a modest amount of demesne troops. The income isn't too shabby either, and it's affected by having your steward collect taxes in the republic capital (at least while you're doge).
How does one reform a pagan tribal nation into a merchant Republic? have absolute authority, port city as capital.
I don't know if you can do it with a coastal city, it may need to be a coastal tribe with an upgraded market. You get an "adopt republic" decision in the intrigue panel, which upgrades the capital tribe to a city.
In other words I don't think it's enough to conquer someone else's civilized city, even if you make it your capital. Also, I think you have to reform the religion if you haven't already.