It does not make sense as a strategic weapon but as a theater weapon it does.These are definitely not strategic nuclear delivery bombers. Maybe useful against nearby targets in case of nuclear war but only India is a nuclear power within reach of H-6. There is no real point to deliver nuclear strikes against any other potential adversary. For actual nuclear targets, H-6whatever will never even get close enough. The ALBM is unlikely to be nuclear. Nuclear opens up pandora's box and the entire point of H-6 deployed towards focusing on the eastern and south eastern directions are more focused on air launching anti-surface weapons (mostly anti-ship) in a clear effort to target carriers. ALBM may be useful against American bases all around China and maybe developed against surface vessels.
You could put either a conventional or tactical nuclear warhead in it and use it to strike enemy naval task forces or land bases.
The extra range you get with the missile allows you to strike with the bomber outside the envelope of enemy air forces or air defenses.