Letting go of the belief they should control everything, mainly by wielding a big stick when the departments need money, will be hard to give up.
It will, however, mean that education, health, etc, get even less attention and money.
It infuriated me when we were all being forced to cut work and staff that they had teams in HMT replicating work other departments did.
I once briefed a Treasury Minister, who passed it on to her own 'experts', who then contacted me to ask me to explain the basics of the topic, ie my area of expertise, so they could decide whether to advise her to do what I'd asked her to do.
I was stunned by the number of staff they had doing our jobs, badly.
Another time a Select Committee asked me why HMT had issued a report about my work area with an analysis that we'd clearly said in a methodology book should not be done with that data. They'd not bothered to consult us.