It's just annoying to see the numerous steps for each secrets on all characters when I have no intent to re-do them. Once was enough, thanks.

Most visible 'Secrets' steps use hidden Quest tracking from Blizzard to track in ATT. You likely want to enable a different ATT Profile on alt-characters which includes Account-Wide Quest tracking to ensure that those no longer show up once one character has completed them.

Eventually we plan to split this type of quest-tracking into a separate tracking type as well.