The existing badge system has a very low distinction between tag edits and more general edits (i.e. edits that also modify the body or the title of the question). There is already a badge series that rewards editing activity: the Editor / Strunk & White / Copy Editor series, which requires 1 / 80 / 500 post edits. That said, the Copy Editor badge explicitly disregards tag-only edits.
In addition to this, it's important to mention the Explainer / Refiner / Illuminator series, which requires users to both edit and answer the post at roughly the same time. As Stack Exchange badges go, this is relatively recent, having been introduced in 2014.
It is an interesting observation that tag-only edits are not rewarded all that much within the existing system: there is only a bronze badge, Organizer, awarded for the first tag-only edit, and that's it. There is definitely an argument to be made that this should be expanded to a full bronze / silver / gold series, since re-tagging is one of the key ways to keep Stack Exchange sites well, uh, organized. In keeping with the numbers on the other series, I would put the silver and gold tiers at something like 100-500 and 1000-2000 tag edits, respectively. If the goal is to reward retagging beyond that, then the gold badge could be made multi-earnable, in the same way that the Steward badge for completing review tags is since last year. These numbers might sound low as compared to the volume of tag edits that you've mentioned in the question, but it's important to emphasize that gold badges should be accessible to everybody, and should not require a decade of activity (at levels that far outpace everyone else) in order to get them.
If you want to propose this, then this site's Meta is not really the place to do so, since it is part of the core Q&A engine that powers the entire Stack Exchange network; as such, the correct place is the network-wide Meta Stack Exchange. And, indeed, a similar discussion has already taken place, at What should we do with the Organizer badge?. (To provide some useful context, Shog9 was an SE Community Manager at the time, and was and remains one of the most knowledgeable and influential voices in how the Q&A engine works and how it interacts with its human users both individually and collectively.) One of the key points raised there is that re-tagging can be relatively easy to abuse, so one needs to be careful not to over-incentivize it.
So, if you feel strongly about this, I would encourage you to think of ways that the badge progression can be specified without over-incentivizing behaviour that could be harmful. (And, in doing so, keep performance in mind. It is tempting to say "tag edits that are followed by upvotes" or something like that, but if you scale that kind of complex database lookup to the millions of posts in Stack Overflow, it will break the server farm. Proposals whose performance would break the system simply won't get implemented by the SE dev team.) Once you have such a proposal, you can float it on Meta SE, and see what people say there!
And one more thing: if you do this, don't get hung up on single users. Physics SE has one particular user that does a much larger share of re-tagging than others, but this user has already been amply rewarded and adding shiny bells and whistles at Q&A-engine level just to reward one single individual is not really in the spirit of SE. It is the community as a whole that does the work, and it is definitely good to have rewards for behaviour by anyone that benefits the community, so things like badge proposals have much better chances of being implemented if they're pitched within this spirit.