I wonder if the seeweed is naturally Monsanto Ready and we could harvest this gene for a green room implementation to subvert the grip they exert over their crop lines.
But outside of taxonomy, it's not incorrect to call them plants.
Also, I'm not an expert, and I know Wikipedia isn't the most authoritative source, but https://en.wikipedia.org/wiki/Plant#Alternative_concepts seems to suggest that green algae are, at least at times, scientifically considered the parent group of land plants. So there's that, too.
Anyway ya plants evolved from protists. What other groups of organisms do we lump together based on an 19th century understanding of the world? I am amazed by people’s ability to warp the world to their priors rather be bothered to update them.
Ooo, I know this one! Fish! Also, trees.
People love to annoy people with the fun fact that palms aren't true trees, but are actually grasses (hell, grass probably is one too), as if tree doesn't just mean "Fairly rigid plant that will usually grow taller than humans." It's useful to have words to describe categories of organisms based on how they appear to us and their relationship to us (say, "gut flora"), even if they don't describe coherent clades.
Sometimes it's important to know that a screwdriver was developed separately from a hammer and really has a very different purpose and theory behind it, and sometimes it's important to know that they both go in the toolbox because they're both things you hold and use on other things to attach things together.
My hot take is that just because a term develops a more specific, scientific definition doesn't mean that the existing colloquial definition is wrong, it's just a different use of the word. It's ok for you to disagree with that, but it's strange that you're so very dismissive of the idea.
The thing is if all you know is that the screwdriver and hammer go in the toolbox, you lack a functional knowledge of those tools and therefore the skill to use them. I for one am confident that you are capable of understanding that while plants and algae are both living organisms, they are functionally, ecologically, evolutionarily, and taxonomically different. The layperson so married to their colloquialisms need not worry about too much detail, yet may benefit from the knowledge that algae are not for bashing nails and plants are not for driving screws. Alas you may wish to know which of the sea you may eat raw or which might seasonally give you a nut flour. Or you may more easily grasp the functional and ecological role of microalgae, armed with the background understanding of their distinction from trees and grasses, should you encounter those creatures. And I hope you do, since you are relying on them to live.
In any case, in my experience, the greater people’s understanding of natural history and their ability to name the organisms in their environment, the more likely they are to see, appreciate, and value the rich mosaic if life around them. The benefits of that are grand for the individual even if they don’t bother connecting the dots on the science.
Colloquialisms are great. But suggesting we all permanently adopt and maintain a state of ignorance because a certain subset of humans had a term, I dunno.
What’s the fish one?
To again quote Wikipedia,
"Tetrapods are descended from fish, so in a break from the long tradition of grouping all fish into a single class (Pisces), modern phylogenetics views fish as a paraphyletic group that includes all vertebrates except tetrapods. To treat fish as a monophyletic group, one would have to classify tetrapods as a clade/subgroup of specialized fish, which would make "fish" and "vertebrates" synonyms."