Following upcoming elections, it may be worthwhile for the Chareidim to join a left-wing government if it is willing to grant Chareidim a draft exemption and is otherwise helpful and accommodating towards the needs of Chareidim.
There is nothing inherent about the right that ties Chareidim to them.
The left includes Yair Lapid. If B&W splits parts would join a Likud coalition so the question does not start. Besides, there are there issues such as restoring the balance between the Knesset and the Supreme Court (which created the mess by striking down the old law).
Bibi Netanyahu is no better than Ehud Barak. If a better deal can be achieved with the left, then that’s a better outcome than a right-wing government.
The left has had that option for years. While some Hareidim are super-hawks, others are super-doves. On most economic issues, the hareidim are much closer to the left than the right, and in fact hareidim views are to the left of most Israeli socialists (all for liberal benefits, especially for large families, and not at all concerned with paying for them). However the Israeli left tends to be fanatically anti-religious (remember that an “ikar” of socialism is militant opposition to all forms of religion).
The left offered charedm better deals in
1990
1994
2009
Charedm turned them down
with the one exception of 1999 & they walked out pretty fast over desecration of Shabbat