I'm saying small blooms happen, yes, but not tank ending ones. Over time, they correct themselves and people usually give up before that happens. It usually takes 3-9 months for a freshwater windowsill tank to reach solid equilibrium, and if you give up early, that's on you.
Therefore it's absolutely possible to run stable a sunlight tank, though you do have to keep in mind it won't behave like your usual domestic tanks. Sunlit tanks will always have a wild and unpredictable element to them- both good and bad. They do have real limitations- sensitive creatures and things need not apply. But if something can handle the instability you're met with a fantastic beast much more akin to the wild version of it.
The way I "run" windowsill tanks means that nature rules this tank. There's no dabbling in dosing. Algae cleaning is minimal- I've never had it not self correct and self clean over time. If you can't handle leaving things will enough alone- it's not for you. Set things up well in the start and see how it plays out over time is the name of the game.