Removing a shield counter in this way isn't the same as regenerating a creature.

If a permanent that would be dealt damage has more than one shield counter on it, that damage is prevented and only one shield counter is removed.

A creature with a shield counter on it may still be destroyed by state-based actions if it has damage marked on it equal to its toughness or has been dealt unpreventable damage by a source with deathtouch.

Shield counters don't prevent players from sacrificing creatures.

If a permanent with a shield counter is dealt unpreventable damage, that damage will be dealt and a shield counter will still be removed.

For Elspeth's first ability, its controller chooses flying, first strike, lifelink, or vigilance, then that counter and the +1/+1 counter are placed on the target creature at the same time.

“Shield” is not an ability that creatures have and shield counters are not keyword counters. If a creature with a shield counter loses its abilities, the shield counter will still protect it as normal.