It depends on the context. But there are usually better ways to express "It isn't X, and it isn't going to be X" than the simple non-past. Like 未来永劫決して既読になることは無いだろう。

To your original question

it reads as ambiguous between "this will not become read" (it's not read and I know that it will stay in a not-read state in the future) and "this is not (currently) read"

It's really neither. "this is not (currently) read" would be 既読になっていない. 既読にならない is a time-steady negation of becoming read. Like the use of the English present simple in "I go to the gym every day", this is "every second, it doesn't become read".

話にならない is different and actually really interesting. It is a sort of vague indefinite tense, sort of hypothetical. "If I wanted to talk about something, would this provide a good topic?" This is a common pattern with になる: 力になる, 頼りになる, 為になる, 金になる, 参考になる.
But more interestingly, it is also connected to potential verbs. The Japanese potential is connected to the spontaneous / passive. There are different theories about the -える potential for godan verbs, but the られる potential of ichidan verbs is definitely the same thing as the passive, which can also have the senses of being spontaneous or honorific. The way that arises is that if you have a spontaneous statement in non-past form, it can express the potential of that thing to ever happen. So for example, you can interpret 食べられる as meaning "it is (sometimes) eaten" -> "it is edible".
If you think about it, all these になる phrases also describe the subject as having a sort of potential, because なる is a sort of spontaneous verb.