One measure of the expansion of the Vice President's role is the increasing prominence of the vice president's staff. Under Carter, the Vice President's Chief of Staff also became an Assistant to the President and performed numerous tasks on the President's behalf. Still much of Mondale's influence came from having allies on the President's staff. The same was true of George H. W. Bush, who during Reagan's first term benefitted enormously from having his close friend James Baker serving as the President's chief of staff.
But under Gore the formal integration of the Presidential and Vice Presidential staff continued. The VP's chief of staff was again an assistant to the President. However, previous National Security Advisors to the Vice President (VPNSA) had had a lower profile. This changed, Gore's VPNSA Leon Fuerth was by most accounts present at most major National Security Council meetings and was an intergral part of the decision-making process.
This was continued (and probably expanded) in the Bush Administration, where Cheney's chiefs of staff also held the rank of advisor to the President.
But this integration has reached a new level in the Obama-Biden administration. First are the number of people with strong links to Biden in the West Wing. But also, according to the invaluable Plum Book, besides Biden's chief of staff, there are five Biden staffers who also hold the rank of Deputy Assistant to the Vice President (including the chief of staff to Jill Biden) and two more who are Special Assistants to the President.
But a picture tells a thousand words. In the now iconic picture of Obama and his team in the situation room monitoring the raid that killed Osama bin Laden, indicated in the picture with a big yellow circle and arrow (helpfully added with the app Penultimate) is VPNSA and Deputy Assistant to the President Antony Blinken. He may not be in the front row - but he is in the room. And in government, once a position/procedure/protocol is established it goes on forever.