While on the subject of this, I would recommend obliterating any of these "relative" general tags. The century tags give you exact periods. World War 2 happened at a very specific time. The Middle Ages, while disputed on the exact length at times, are still a very specific period of time that is defined as being that time. These all work as tags because when someone looks at that period, they know when it is supposed to be.
The existence of this question is evidence to the contrary when it comes to periods where their definition is relative to the current period. ancient-history is actually more problematic because of its nebulous nature - when does ancient start? It is simply not an understood term.
Similar tags include early-modern and contemporary-history, and these illustrate more strongly the issue with relative general tags since their period of operation is likely to be affected in near future of this website. Early modern extends how far back? In a few years, does it still count as early modern, will we have to remove tags?
Tags are not meant to be dynamically changing - they're intended to be a static descriptor that helps you strongly identify what a question is about. If a tag's validity is affected by the passage of time because it is relative to present day, then it is extremely suspect as a tag. This kind of effect is a bit more visible on other sites like Gaming, where we have "old-games" and "retro-games" tags that just no one is sure what counts as that because of how fast the game generations span out. On History, it'll take centuries to affect things like ancient-history, but it still is far more useful if there is a more definitive descriptor about the actual era in question.
On a side note, there is ancient-greece. I'm not as strong a history buff, so I don't know if there's truly an accepted and solid period of time that is "Ancient Greece" that isn't just "Greece really long ago". If it is an accepted and solid period time that is not defined solely by its relation to present-day Greece, the tag works.