I am not a tax expert, the opposite in fact, but if the thresholds are raised does that not flow on as tax cuts to all levels given the way in which our tax liability is assessed?
You could argue that point. Earners in the upper brackets will certainly benefit the "most" (in absolute terms) from lower bracket adjustments - but the dollar value of that benefit is capped, and relatively speaking they will see a smaller percentage of their tax bill being reduced than a lower income earner.
Simple example: A tax rate 10% up to $10k and 20% over $10k. New policy, sees the bracket adjust up to $20k.
A person earning $20k previously has a tax obligation of $3k ($1k from the lower bracket plus $2k from the upper bracket) They would get a tax cut of $1k. (or a 33.3% reduction of their bill.)
A person earning $40k previously has a tax obligation of $7k ($1k from the lower bracket plus $6k from the upper bracket) They would also get a tax cut of $1k. (or a 14.3% reduction of their bill.)
When you get into the extremely high-earner realms, the $1k saving becomes almost insignificant in the context of the total tax liability... (but you could still legitimately "call it a tax cut for the rich" if you wanted to.)