Depending on what fruits you're talking about, leaving it to rot out in the open could take weeks up to months (e.g. bananas or orange peels take very long, apple peels on the other hand rot faster). This is not desirable for public spaces. Please always put your waste into the next bin when you're in park or similar area. If you're out hiking, you might leave the quickly rotting waste (tbh I do so with apple cores or similar). Have a read here, they explain quite good, how leaving organic waste out in nature is not a good idea.
If you're concerned about non-correct waste disposal, put the fruit back into the packaging you had it in and throw it into the correct kind of bin at home.
Also, a really nasty side effect of leaving organic waste out in the open is that it attracts pests, be it roaches or rats or similar animals. To you the waste is not edible, but to them it's quite fine. The more waste is left out in the open, the more pests are attracted, spoiling the recreation for everyone using the park.