This could inspire some to take their ballot more seriously. Sometimes it isn't so much that players build up momentum, as Bert Blyleven did. I don't know if Blyleven would have impressed as many as a Hall of Famer by his 10th year of eligibility, although there could have been some that didn't vote for him because they would be able to vote for him next year. Maybe he would have made it in his 10th year because there was no tomorrow, so to speak.
Of course, there are players in recent years who are dropped off the ballot because they don't make the 5 percent who will be elected by the Veterans Committee. The BBWAA has always overlooked deserving players, such as Nellie Fox. Luke Appling failed to make the 5 percent when he was first on the ballot, but the writers ended up electing him.