Beside my concerns about what Venice's puppets do/don't build, as a player you can make Venice quite strong in the right conditions. Unfortunately, this is much more of a problem for AI. As player the most important thing I do is to ensure the 3 Colonia Puppet cities are up & running as soon as possible, as if not you can be struggling. So, I build Pyramids for free settler, then go authority for another free one, as well as Trade to get the free one there. By doing that you should be able to get all three up & running up the time AD comes around if not before. The AI though is extremely unlikley to do this, as building the Pyramids & going Authority is not something Venice goes for, which I understand, as a Tradition sort of civ. So, to obtain the three puppet cities the AI has to hone in on to trade orientated techs to enable itself to obtain the GM to build these. By the time they have done this it is likely to be the Medieval age or further, with all prime sites gone, & putting Venice in trouble, if they haven't already been put under.
I am not sure what is the answer to this, but there does need to be a way for Venice AI to get their puppets up quicker to give them a better chance of surviving then prospering.