“Chareidim gave Likud the majority in ’77 and ’81, saved Shamir in ’90 even though Peres offered them the better financial deal, and gave Netanyahu his majority in ’96 and ’09.”
Not true for 1977. The government consisted of Likud (45 MKs), DASH (15 MKs), and Mafdal (12 MKs). That’s 72 MKs out of 120. No charedi ministers or deputy ministers. (That was the best showing for religious Zionists until this past election.)
Also not true for 1981. The government consisted of Likud (48 MKs), Mafdal (6 MKs), Tehiya (i.e. Geula Cohen, 3 MKs), Telem (i.e. Moshe Dayan, 2 MKs), and Tami (i.e. Aharon Abuhatzira, 2 MKs). That’s 61 MKs out of 120. No charedi ministers or deputy ministers.
Charedim did save Shamir in 1990 — but he only needed saving because they had supported the only successful no confidence vote in Israel’s history. Charedim gave Rabin his majority in 1992, abandoning Shamir for the second time.
Charedim were indeed the margin that gave Netanyahu his majority in 1996, but Netanyahu had won the popular election and was guaranteed to be PM no matter what. The same thing happened in 1999 when Barak won the popular election and charedim joined the government.
The only time that charedim did make the difference among the elections you listed was 2009.