The Ashkenazi "Union of Torah Judasim" remains one block despite the internal conflicts. It is composed of the Litvak Degel HaTorah and the Hassidic Agudat Yisrael and each one is in turn composed of various fractions with internal struggles but still they remain in the same block and united in their goal of leeching the maximum amount of pork out of the working tax payers.
If one Hassidic court would try to go it alone they know they are going to fail and be left out of the scavenging so they stick together no matter how much they despise each other.
Shas has somewhat different dynamic in that most of their voters are not zombies who automatically vote to the party and candidate their rabbi orders them. In shas the functioneers like Deri and Yishai run the show and Rabbi Yosef was basically a figure head especially in his latter years. Sure his word was like law but he spoke the words that the corrupt confidants put in his mouth. Sometime he didn't speak at all, he was just rumoured to say this or that thing and that was enough.
Now it is likely there will be less cohesion and more open battles that once only went on behind the scenes but the fact remains that anyone who will try to run alone will fail and be left out just like all the others who tried and failed in the past— because they will be running on image alone and will not have any material incentive to offer for their potential voters.
UTJ has been known to break up & then re-unite when convenient & indeed there are divisions in the the Litvish world since Rav Eliyashiv's passing.
Shas will have less cohesion & the non-Chareidim will defect to other parties IMHO.
The Mishichistim were trying to run with Baruch Marzel & ended up with Ben Ari who was the candidate of Shalom Dov Wolpo & Baruch Marzel. In the end Ben Ari is out & B"H to that.
Only time will tell if Shas will fall apart post Rav Ovadia.