Won’t one be hurting the careers of students by not publishing in the venue with the broadest audience?
The one problem I'm aware of is those who want to get positions in universities that don't know how the field works, because their selection committees tend to complain that you have no journal papers. If that's your plan then you can submit to journals such as CL. But again, that's not where the broadest audience is.
However, I do not expect that the audience that matters will not have access to your work in some way, even without open access. If your university is a good one, they will have subscriptions. Plus, there will be networks of researchers illegally passing around documents. Rather, closed access hurts researchers at less privileged institutions and the general public, as they are unlikely to gain access.