After 55 years, January 20th, 2023 will mark the first time since 1967 that no member of the Cheney, Clinton, McCain, or Bush family will hold elected or appointed office in the federal government of the United States of America.
Liz Cheney would leave office on January 3rd, not January 20th. There is no reason to believe Cindy McCain will leave office in 2023, so there will still be a McCain holding appointed office (Ambassador to the UN Agencies for Food and Agriculture).
There have also been four gaps in the last 55 years; one as recently as 3 years ago. I listed at the bottom when each family was in office, but the gaps are:
Aug 25th, 2018-Jan 3rd, 2019
Jan 20th, 1977-Jan 3rd 1979
Jan 18th 1973-Sept 26th 1974
Jan 3rd, 1971-Mar 1st, 1971
It is interesting that three out of the four families you listed were Republicans. The Clintons, husband and wife, were in office for 20 years, which does not seem like an extremely large amount of time. It has not been intergenerational.
Cheney Family = Dec 18th, 1974-Jan 20th, 1977; Jan 3rd, 1979-Jan 20th, 1993; Jan 20th, 2001-Jan 20th, 2009; Jan 3rd, 2019-
Clinton Family = Jan 20th 1993-Feb 1st,2013
McCain Family = Jan 3rd, 1983-Aug 25th, 2018; Nov 5th, 2021-
Bush Family = Nov 4th, 1952–Jan 3rd, 1963; Jan 3rd, 1967–Jan 3rd, 1971; Mar 1st, 1971–Jan 18th, 1973; Sept 26th, 1974-Dec 7th, 1975; Jan 30th, 1976–Jan 20th, 1977; Jan 20th, 1981-Jan 20th, 1993; Jan 20th, 2001–Jan 20th, 2009