I’m pretty sure that did happen.
Henry VII’s backdating of the start of his reign to the day before Bosworth Field wasn’t just about putting current nobles under threat of treason trials (although it was mostly that), it was also a statement that Richard III was not a legitimate monarch. Indeed, Henry VII made one of the first acts of his first Parliament to have the Titulus Regius, through which Richard III had claimed the throne, declared “be void, adnulled, repelled, irrite [invalidated], and of noe force ne effecte,” and then had every last copy he could find destroyed.
And you had similar things happening throughout the Wars of the Roses, where both sides presented very different arguments about the correct line of succession. When Richard Duke of York made his attempt to claim the throne of England in 1460:
York went to the House of Lords and formally presented his demand to be recognized as the rightful King of England, presenting them with a document detailing the succession of the Kings of England, and specifically how as the descendant (on his mother’s side) of Edward III’s second son, Lionel, Duke of Clarence (in addition to being the direct descendant of Edward III’s fourth son, Edmund, Duke of York), his claim to the throne trumped that of Henry VI, whose grandfather had usurped the throne from Richard II, despite being the son of the third son of Edward III.
There were different Lancastrian versions of the rolls of succession – Henry VII kept Edward IV on his rolls because of his marriage to Edward’s daughter but other Lancastrians considered Edward IV an attainted usurper, which led some of them to prefer other Plantaganet lines (the de la Poles had some impressively contorted rolls of succession in their back pockets for the day that never came when they would unseat the Tudors).
There were some impressively conflicting Yorkist versions: rolls drawn up by George of Clarence that recognized Henry VI and not Edward IV because of a 1470 declaration by Henry VI declaring Clarence his heir if Henry VI died without issue (Edward IV being attainted at the time) and in a stunning display of hypocrisy also argued that Edward IV’s contract of marriage to Eleanor Butler meant that his marriage to Elizabeth Woodville wasn’t valid, so that George was Edward IV’s heir too! (And that’s in addition to the rolls Clarence proposed claiming that Edward IV was not the son of Richard Duke of York, making Clarence Richard Duke of York’s heir.) The Woodvilles responded by rolls which returned the favor by barring Clarence’s son George due to Edward IV putting Clarence under attainder. Richard III under Titulus Regius got Parliament to sign off on the Butler marriage theory (as well as the attainder on Clarence and his kids), and harshly critized Edward IV but still otherwise followed the Yorkist line of succession. One major reason why Henry VII had that law obliterated as much as possible was that it disinherited Elizabeth of York, and thus touched on his own claim to the throne.
As to why Henry II didn’t strike out King Stephen, that had a lot to do with how the conflict ended: the Treaty of WInchester made Henry FitzEmpreess his successor and required Stephen’s son to do homage to Henry, in return for Henry doing homage to Stephen. Not only did that create an embarrassing situation for Henry if he declared that Stephen had never been king – which would have meant that Henry had done homage to a usurper – but it also created a situation in which Stephen’s legitimacy had a direct bearing on whether Stephen’s son’s homage to Henry (which precluded William from making a claim on the throne) was valid. Also, the Empress Matilda had made herself very unpopular with the nobility of England, and Henry wanted to win over the barons who had opposed her; removing Stephen from the rolls in favor of his mother would reopen all those old wounds. Much more politic to simply side-step the issue altogether, and emphasis his descent from Henry I instead.