I have adored Venice since 5. After playing and winning about 7 games on king/emperor, I have some input though, with the utmost respect attached. Sorry its a bit wordy.

The first time I played, I played to his strengths and ran home with a Culture victory rather handliy, around turn 160 on Online speed.
Every time I have played since, I have been attempting a Science victory, and here is what I have found.

1.Venice is a hard starter. He needs abundant resources to be productive, have food and housing, and needs at least some variety to them. Venice also needs to start on a coast tile, and that has to connect the main oceans somehow if you want an effective Navy.
2. Venice can basically ignore having great works, if they have a few wonders, a Fandaco, and 10+ Trade routes, and still attain a culture victory.
3. Venice can focus completely into science, and what few science wonders there are, and can still lose to his own culture.
4. If Venice builds the Venetian Arsenal, it is absolutely Game Over for anyone who wants to tangle on the Seas with anything short of planes.
5. Venice almost cannot lose the culture victory if he is trying, and his start is decent.
6. It is difficult to attain any other victory than cultural as Venice.
7. You can achieve all of this without taking any other cities simply with a legendary start(Which with me and a lot of people is just a standard way to play) as well as completely ignoring the Satellite Broadcasts, Heritage Tourism, and Online Communities policies.

I conclude that there are two reasons for Venice being tied down to the Cultural victory:
1. Since Venice has the lowest population, his threshold for attaining the cultural win is always the lowest, and increases the slowest.
2. The x3 Tourism pressure bonus to Mudas. (Note that I haven't tested this by sending all of my trade routes to City-States, but as that's not something that most people do, I didn't figure it was a good test.)

Given this information, I have 3 changes I would recommend:

1. Decrease the tourism pressure bonus from x3 to x2, or even x1.5(As there are also policies allowing one to increase their tourism pressure to other civs. Additionally, one will has the potential of having a 17+ Trade Route Capacity, so even with that nerf, and less trade routes, if you're really trying to win that way, you can. Whereas if you're not trying to win that way, you wont pressure everyone into the culture win anyway.

2. Make Venice always begin on a coast tile. It's historically accurate, and its saves a few restarts, and allows the player to make the most of their naval bonuses.

3. Give the War Galley it's own promotion tree, if that's possible. Preferably one that allows it to be more effective against land units, even if to balance it, you'd have to take away some bombard strength with the same upgrade. One can produce War Galleys at an incredible rate either through purchase or training, starting from potentially the Ancient Era, and its easily possible to get to a point as Venice where all you really can build is units/ships, so by the time you get Square Rigging, you're likely sitting on a navy of 12-14 Frigates(Compressed with Nationalism or Mobilization) which feels a little unfair. If they have their own promotion tree, they can be individually effective during their most effective era, but mostly useless afterwards, much like nearly every other unique unit. Additionally, it will at least in the early game create a varied and capable Navy, without absolutely breaking after Square Rigging is researched.