Any party advocating Council Tax reform would be more likely to get my vote; the current system is illogical and unfair and needs reforming. The Conservatives with long memories know what happened last time they tried a radical reform, and presumably this spills over to the other parties who will be equally terrified of ending up being seen to make the same mistake.
Local authority funding is a mess, more so after the various Conservative governments since 2010, but it doesn't figure highly on voters' interests I don't think. Any sensible reform would probably also mean significant increases for London residents and reductions for places where "levelling up" might apply.
I guess that last point would be key, would a reform lead to lower CT rates outside the capital? If so it may be seen as a positive (although that would depend on the impact on local services), however people tend to be more suspicious of reform leading to higher taxation. So if reform is something Labour are mulling over for some time in the upcoming term, they probably now need to make that clear now otherwise the Tories will weaponise this issue.
It'd be intensely problematic because Council Tax is based on some kind of historic property value, and if the only change were to update this base then it'd increase the tax in London and decrease it outside London, but then London councils would have more money and others less, so there'd then need to be some kind of transfer to make up the differences. I don't see that easy at all. The other problem is that those who currently pay "too much" (maybe me) just live with it, whereas under a reform anyone hit with a 20% increase would make a lot of noise.
So it's probably just in the "too hard" category for politicians.
But, then, so is everything related to "levelling up" which was just a Boris soundbite with no substance. Gove probably tried. But they don't really care or intend to do anything, and the "red wall" is now lost beyond salvation anyway so there's no political capital in it either.
There are some misunderstandings here about local government finance in general and council tax in particular.
Before the start of each financial year, each local authority sets a budget of what it plans to spend and how that will be funded. That includes its council tax requirement, the amount it needs to raise from council tax.
At the same time each billing authority calculates the council tax base, the number of properties in each council tax band, and in particular the number of band D equivalents, each of the other bands being on a fixed ratio to band D.
The band D council tax is then calculated by dividing the council tax requirement by the number of band D equivalents, and the other bands by applying the fixed ratios to the band D number.
Reform of council tax on its own does not affect each local authority's council tax requirement, that still comes out of the budget setting process. The main impact of changing the council tax bands, either by a property revaluation, and/or by changing the ratios between the council tax bands, is to change how the council tax requirement is distributed amongst properties within each local authority.
In particular it would not directly redistribute any funds from one local authority to another. That happens all the time through grants from central government. But council tax reform would change the council tax base, and there might be an indirect effect if the council tax base is part of any of the grant distribution calculations.