The "mistake" happens so often, partially because "segway" is a much more straightforward spelling if one has only heard the word said aloud, that I think it will eventually become the actual way it is spelled!
Looking it up in https://en.wikipedia.org/wiki/Segue they even warn about that!
That's precisely how language changes over time. Language is not a strict set of rules. It's based on understanding and consensus, so sometimes things that are "wrong" do end up being accepted.
I suggest this as a great introduction into what languages are and how they evolve over time https://www.amazon.com/Language-Families-of-World-audiobook/...
How does this mistake happen so often? Can you explain people's thought process a bit? Is it just: "Something something 'seg...' ... ah I know, I will simply use another random word that starts with the same 3 letters and doesn't make sense in this phrase!"?
Also this is the first time I see it.
Pronounced correctly, “segue” sounds just like “Segway” – not like “seg-oo”, as you might have assumed.
I am sure people will make the mistake, as they sometimes do today. But it is a mistake, and will likely be recognised as one.
It is likely that the language gets more cemented by automatic spelling and grammatical correction, including using AI. For example, there are a number of grammatical and spelling changes that have been cemented by American spelling/grammar checking programmes ie. by MS Word.
I did not imply that at all. I said sometimes, so it's not that absurd that it could happen. It does happen though, and a quick google search will give you pages of examples.
With machines looking over our shoulders now and so much of language being typed instead of handwritten, odds are such drift might actually decrease in English... On the other hand, the introduction of AI leaves an interesting avenue for people to begin acting as if something is common usage and have the AI begin confirming that as common if it consumes that action. And then, of course, there's the effect of the machine itself... Most of us have a way to type "résumé", but we don't bother because the machine makes it too much work to do so, So the alternate spelling without accent, which was called out in my high school days as wrong, has fallen into common usage in a generation of people having to submit their resumes online (example: https://www.linkedin.com/help/linkedin/answer/a510363).
In more forgiving of mixing up homophones, even if one of them is a registered trademark (Segway).
I suggest you yourself take a second and explore why you think being smarmy on the internet is a way of getting people to agree with you.