If the railway crosses a public right of way, then that right of way can be exercised. The alternative is to close the right of way (i.e. the crossing) and provide an alternative right of way (i.e. a bridge).
Now of course, this assumes people are going to be sensible and treat the railway crossing with respect. We've had these crossings for hundreds of years, with appropriate signage (most of the time) but sadly, society has changed and people just don't think, or care about their own actions these days, and the consequences of their actions. I'm sure this sort of thing didn't happen before the invention of mobile phones/social media etc.
As a well-used crossing, I think NR are right to consider alternative means in order to retain the right of way, but it has to be sympathetic to the local area/landscape