Generally, they do not, all plants, even the nice ones in our tanks have algae, you just cannot see it with the naked eye.
The question is also WHEN you see the plants without being covered with algae. Early in the season, the new growth is clean and nice, late mid summer, languid water full of hair algae on top is common.
If you walk down a stream, say Putch Creek in Yolo County CA, you will find nice beds of Euasian milfoil, Curly leaf pondweed, sago pondweed, Elodea....and a few feet away, algae mats, walk a ittle farther, you find them both mixed together, walk farther down, the plants are nice and clean, and the algae is not around. A bit farther, you find a lot of matted algae covering the side of the entire stream, farther down a big green murky pool you might only see 1-2 ft at most.
All within the same stream, under the same sun, same nutrients etc.
Why do elephants survive if mice/rabbits are also herbivores and live in the same habitat? Why are there forest vs herbaceous weeds in the same habitats?
They have different niches and advantages. Most algae are seasonal, plants can be or not. Water levels also change and many, if not most, of the plants we keep are amphibious.
thats pretty much it in a nutshell. i have never encountered plants that dont have some kind of algae on them. i have collected plants in all four corners of north america and have always seen algae somewhere. sometimes the plants are so covered its a wonder they survive to the next year, at other times, completely free of algae.