I think the key difference between a counsellor mentioning suicide and passing a high bridge isn’t a difference between emotional and physical enabling of suicide: it’s that a counsellor can actually have some positive effect.

A counsellor can ask a suicidal person why they’re considering suicide, and attempt to convince the counsellee that killing themselves isn’t their only option. A bridge can’t do that: it just panders to their blinkered, suicidal desires.

A bridge is like a counsellor saying ‘go on, you may as well; killing yourself is easier than you think!’ I fear that might put the idea into the caller’s head, or make the idea seem more acceptable…