Merely non-HTML tags wouldn't suffice. If this was implemented it should be any tags that aren't allowed in posts like
<div>. I see people do this all the time:
I want the to change depending on the value.
I want the <select> to change depending on the <input> value.
I habitually check the post source by clicking  whenever I see an awkward sentence like that.
One side of me wants to disagree with this request, since it should be pretty obvious there's a mistake if you actually preview your post before hitting submit, which you should, always. I'm not sure if this would encourage laziness.
On the other hand, I see a lot of posts about HTML get downvoted along with "Code? What code?" comments because the code is totally hidden. The burden is on the poster really, but maybe a warning would be a good thing for overall quality and would help newer users get used to formatting correctly.
Possible alternative solution: Would it make more sense just to output the brackets on disallowed tags as entities, so that they appear? For instance if I typed
<input> without formatting it as code, it would appear as <input>. It would still be unformatted, but better than being invisible. Is there any point in hiding disallowed tags in the first place?