I believe you're right, even though I don't have any evidence except for my own experience.
This issue becomes very clear when you see how many ways there are to express a simple concept like linear regression. I've had the chance to see that for myself in university when I pursued a bunch of classes from different domains.
The fact that introductory statistics (y = a + bx), econometrics (Y = beta_0 + beta_1 * X) and machine learning (theta = epsilon * x, incl. matrix notation) talk about the same formula with quite different notation can definitely be confusing. All of them have their historical or logical reasons for formulating it that way, but I believe it's an unnecessary source of friction.
If we go back to basic maths, I believe it's the same issue. Early in my elementary school, the pedagogical approach was this:
0. only work with numbers until some level
1. introduce the first few letters of the alphabet as variables (a, b, c) - despite no one ever explaining why "variable" and "constant" are nouns all of a sudden
2. abruptly switch to the last letters of the alphabet (x, y, z), two of which don't exist in my native language
3. reintroduce (a,b,c) as sometimes free variables, and sometimes very specific things (e.g., discriminant of a quadratic equation)
4. and so on for greek letters, etc.
It's not something that's too difficult to grasp after some time, but I think it's a waste to introduce this friction to kids when they're also dealing with completely unrelated courses, social problems, biological differences, etc. If you're confused by "why" variables are useful, why does the notation change all the time, and why it sometimes doesn't - and who gets to decide - this never gets resolved.
Not to mention how arbitrarily things are presented, no explanation of how things came to be or why we learn them, and every other problem that schools haven't tackled since my grandparents were kids.