That's an interesting, and correct observation. Let me explain:
The solution would be to disable page-cache for this specific page. Although it might just take 1 second more to generate the page, that is much slower than cache, which is likely below 0.1 seconds. Simply a poor compromise. It would have to re-process the entire page for all visitors, on each visit.
To be honest, none of these options are favorable, so this topic would likely be tagged "technical logical limitation".