Late-game Tristana is actually strong in URF, but she has a terrible laning phase against pretty much all of the OP picks. Taking her to a solo lane is not a very good idea for that reason. Late game though, she has tons of mobility and her ult letting her create space between those OP picks and herself, and she brings the ability to destroy an inhib tower in under 2 seconds, dragons and barons also go down super fast. You only need berserker's greaves and max Q to have permanent max attack speed with damage amplified by spam of her E-bomb (I haven't tested if you don't even need the greaves. I already go bloodthirster first for survivability, I wouldn't mind defensive boots too.) Her dueling remains poor against all the OP picks even into the late game, but she brings teamfight presence and objective securing to your team. Getting farmed up isn't usually too hard because of having great wave clear and the fact that most of both teams are busy chasing solo kills.
TBH, Tristana is the only ADC besides the obvious Ezreal OP pick that I would take into URF. The short range escapes of graves and lucian just don't give enough space between you and that OP assassin gunning for you, Caitlyn is hampered by long cast times so that she can be burst down before her EQ combo animation completes, and immobile ADCs are sitting targets.
On-topic, I agree with the OP. Pick champs for fun. If you find out they are terrible in URF, try another. There are a lot of champs that are decently strong though, strong enough to have a good match. More importantly I think is for people to ban 3 of the OP picks... too often bans go to other champs, presumably ones that the team captain doesn't want to play against on his favorite OP pick. At least if you ban 6 of the 10 OP picks, there's room for a little variety in the teams.