The built in stun that each tank has breaks combos and costs damage, their role stun is the same as ours. Take paladin, as an example: In a fight or flight rotation they need to do goring > royal > royal > goring into ogcd requiescat to maximise dps. If they need to use an on GCD stun, even if it didn't break combo, it would mean missing one goring and requiescat under fight or flight, for a potency loss of over 300 potency (that is if they have to stun at any time during the fight or flight, which is 25 seconds out of every 60). Similarly, if they need to stun during requiescat (12 seconds out of every 60), they lose 20% damage from a cast of holy spirit for ~90 potency lost. Neither of these even consider the impact of losing the GCD.
For them to take the ogcd ability means they lose another role ability, and tanks have many mandatory picks. Provoke is basically mandatory, Rampart is basically mandatory, then you have convalescence, anticipation, reprisal, and shirk. In a party they don't need shirk, in a raid they probably drop convalescence or anticipation. In all cases, dropping an ability for the stun means losing a damage avoidance ability and less safe aoe pulling or boss tanking.
Bard has zero downtime on mobility so running into melee range is almost never an issue. Second wind is a heal, but it isn't a particularly great one and is on a very long timer. If you need a stun then dropping second wind is very likely to be inconsequential.
