I don't believe students subconsciously misread the notation as an exponent with a word in front. I think they are not sure at all how to read the notation!
When using logarithms (whether in a basic, introductory algebra course, or an advanced vector calculus course) I always use parentheses to distinguish the argument of the operation, e.g. $\log_a(b)$. But still, there are always plenty of students who (i) don't know how to read that expression verbally, (ii) don't know how to interpret it conceptually and, consequently, from both, (iii) have no idea how to evaluate or manipulate such an expression.
I try to stress the exponential aspect, introducing examples like $\log_2(8)$ and reading it out loud as, "To what exponent would we need to raise 2 to have 8 as an outcome?" Sometimes this helps. But I even worry that the grammar of that verbal reading of the expression confuses some students just as much! I mean, is this any better: "What exponent do we need to raise 2 to, to get 8 out?" I think not. (And the fact that I picked 2 as the base here only makes it worse; the confusion is just as bad with other bases that don't sound like "to".)
What's even more shocking to me is that, every semester, I find students "solving a problem" and getting an answer that's something like $x=\frac{4}{\log}$. I wish I were joking! But no, their confusion is so extensive that they don't see anything wrong with such an expression, with an "empty" log like that. I typically respond by saying, "This is like writing $x=3+\sqrt{}$ with nothing underneath; it has no meaning." But I so rarely get to follow up with those particular students, so I can't be sure whether that comment helps them better understand the concept.
So, I wouldn't say your concerns are unnecessary; rather, I think the root problem(s) precede confusion about super/subscripts. Below, I list a few things that I believe may be related to this confusion, and try to make some suggestions about how to address them.
- Problem: Poor arithmetic skills, especially with basic exponentiation. If a student doesn't recognize immediately that, say, $81=3^4$, then they're not going to see any sense in the expression $\log_3(81)=4$. It will look like black magic to them. Addressing this: Take the time to show that $3^4=3\cdot 3\cdot 3\cdot 3=81$ when you introduce this example. It will take more time in class, but it will help prevent some from getting lost right off the bat.
- Problem: Difficulty understanding the notion of an inverse operation, or being able to ask/answer a question that probes this concept. Look at the sentences I used above: "To what exponent should we raise ... to get ...?" This seems like a simple question to teachers like us who can move "forward and backward" with operations. But to a student, they're used to evaluating expressions forward, plugging and chugging. This may be the first time (except for square roots) that they face an operation that asks them to "undo" something. Addressing this: Perhaps it's best to introduce the fundamental idea of an inverse operation before tackling exponentials and logarithms. Most College Algebra textbooks I've worked with tend to have Inverses as part of their chapter about exponents/logs, but perhaps we can do a better job of synthesizing all those ideas and presenting them as one.
- Problem: Perhaps $\log_a(b)$ is just genuinely bad notation. I hesitate to say this because I don't have a good proposal for a replacement. But after several years witnessing the same conceptual and procedural errors from students, I truly wonder whether the notation itself is part of the problem. Our temptation is to say something like, "Well, it's just the way we write down the concept; if they understood what it meant underneath, they would understand the notation." Or, we might say, "Well, that's how it's written everywhere; we can't change it now." But I just don't know. Hopefully, someone else can link to some actual research about this idea. Addressing this problem: I don't know. Does anyone have a good proposal for a new notation and reasonable evidence for why it's better for students learning the concept?