If a class is defined by the engagement distance, then I agree with you. I don't think that it should be though. In my opinion a class is defined by the utility it brings to the team, and you can play with different weapons at different distances and still provide the same underlying role. Having closed weapons does not necessarily make the players immediately know what their class does, and I do not think it is a positive thing that we force players to play a certain way either.
Engagement distance is just one (potential) part of the identity and so is the utility it brings to the team. If you're clearing buildings, you're not doing the same job as when you're occupying the high ground and spotting everyone in a large area. Similarly, you won't be healing anyone if you're far way from your teammates. This means that the engagement distance in many cases dictates the kind of utility that you can bring to your team. Whether that's a positive thing is an entirely different question, but in terms of intuitiveness the weapon you play does make an impact.
