Why do you think Labour will never do this?
Because it makes sense but against ideology.
Let's take two single people, both own their houses which are the main parts of the estate. For simplicity let's assume neither will pay care costs.
Person A - lives in e.g. NE, house worth 499k. No partner. IHT is zero.
Person B - lives in London, owns identical house, but worth 1m. IHT is 40% x 500k (above nil band) = 200k.
With new 10% flat rate Person A will pay 50k, Person B will pay 100k (well, their estates will pay).
HMRC will take much more in tax because there are many more As than Bs.
But voters will scream how unfair this approach is because "the rich" will pay less.
What they fail to realise is that people who are to be hit with significant IHT will take steps to avoid it, e.g. Person B downsizing and gifting early, so IHT=0 for them.
And millions of voters who expected their inheritance with no IHT to pay will now have to pay something. So no, I don't think Labour will do this, they are much more likely to introduce this levy and keep IHT, or rename IHT as levy but make progressive to keep the same rate of 40%, so everyone will end up paying more.
ETA: it's a classic example of less tax on broader base brings much more. If you look at our current income tax and and cliff edges - it drives all wrong behaviors and encourages people to work less. It also creates a very risky situation of top 1% paying 30% of all income tax, so some slight shift in behavior leads to significant consequences. Make it more equitable and you'll get more money and boost productivity.