To quote a part of the current policy that was added in a later edit:
[...] we could allow system tags to be edited in without the OP’s input after a Meta discussion agrees that the situation is “safe” to edit. [...]
And to quote the user who suggested that policy describing the policy elsewhere:
[...] The policy exists as it does because we don’t have the best vision on any ad hoc decisions made by individual users and that’s a problem, but this isn’t a decision by any individual user—this is a Meta discussion, where we can gather consensus. [...]
[...] The policy would not allow an individual poster to edit this question, but with Meta consensus [it could be] [...]
[...] This cannot be generalized; we can discuss this question but not any broader category of questions that are in some way “like” this one. A Meta consensus is necessary for this kind of edit.
This answer is not saying that adding the dnd-5e tag doesn't violate policy. Doing so without consensuswithout consensus does violate the policy. This is trying to get at a consensus.
Are any of those likely? We can't truly know (we don't have all the data in the universe).