Ok, I first did not see much use of a BSM tag too, but no I think it can be useful and we should have one for the following reasons:
- I agree with what Matt Reece said in his comment: there's some effect
which is not present in the SM and a question about what it means and
how it can be interpreted, not linked to any particular model.
General things like questions involving bounds on higher-dimension
operators---of which the proton charge radius is, more or less, an
example---would be a good use of this tag
- At the LHC, in addition to very specific searches for BSM physics
which can clearly be ascribed to a particular theory/concept/model
such as supersymmetry or string theory, people do more general
broader searches for BSM physics effects which can not be uniquely
related to a single known theoretical idea, such as extra
dimensions, violations of fundamental symmetries, or more generally
for deviations from the SM one would not yet know how to interpret
them at present, too. Questions dealing with such issues could not be
tagged with string-theory, supersymmetry, etc.
Exactly to fill this gap, bsm is usefull and it would be useful for people who want to ask and/or look for questions which deal with more general BSM phenomenology including more exotic effects, which are not covered by the specific tags denoting BSM theories and concepts we have.