Well, in matters of the English language, grammar and usage thereof, the distinctions between "right" and "wrong" are malleable - but the term "awkward" often applies in doubtful cases - as in this one. The expression "by the time" conventionally signals allusion to an event that has occurred or conditions that have changed or reached some point of finality between a previously referenced time and the time in question. If not "wrong", it can be "awkward" to use "by the time" to signal allusion to stasis. No doubt there are exceptions, and the context may make a difference.