You only have to pay that if you're a day visitor. If you're staying on one of the main islands, you don't need to pay. The place you're staying should have a tourism site ID code, which you can enter on the site to get exemption.
a giant sewer city
I never get why this image is so prevalent. Just visit a month or two before or after the main summer months. May or September perhaps, it's usually still warm, and I've visited many times now and only had a few days when in a few select areas it was a bit smelly. The idea it's common is just plain wrong based on all of my visits.
with no trees
There are trees quite literally everywhere. Maybe not on Rialto bridge, though. Even next to San Marco, there are some nice gardens. Further along at the Biennale, you will see many more gardens. There's also a garden right by Piazzale Roma and the train station. Once you leave the main tourist areas, you'll see plenty of trees pretty much everywhere.
two people per every square meter
Go slightly off season, and actually leave Rialto and San Marco alone once you've seen them. You can walk for literally 2 minutes and go from serious crowds to totally alone from either of those locations.