Honestly, it depends on the matchup. With some champs, I never risk engaging her as her damage, skills, and tankiness are always going to outdo my performance. With other champs, play against her is balanced and amounts to predicting and countering her E and R. And that really seems to be what the community complains about.
Even good players have trouble against her if their champ isn't that great at shrugging off damage and sustaining high damage output. The other main counter is poking her to death with a very mobile burst mage. Warwick is one of the few champs I've seen keep up with her while taking hits.
Playing as illaoi is about timing and positioning. Release your R or E to quickly change the dynamic of the fight. R has helped me win 3v1 ganks, and E can double as a poke that causes squishy champs to disengage. Without those two abilities (when they're on cooldown), she either sacrifices damage by moving away from tentacles, or mobility by staying near them.
In some cases, she can get absurd kills. In others, her mobility and range leave her prone to ganks and pokes. What most people seem to hate is the fact that she can turn a 3v1 into a huge advantage with R; players go to great lengths to stack odds in their favor to kill her, but her kit can counter these strategies effectively. Most other champions don't have this luxury; they must disengage when the battlefield is not to their benefit.
She isn't necessarily OP. Her kit just needs a lot of coordination and some skill to counter.