If suddenly the NHS had a team of "free" genuinely phd-level AGI engineers working 24/7 they'd make a bunch of progress on the low-hanging fruit and modernize and fix a whole bunch of stuff pretty rapidly I expect.
Of course the devil here is the requirements and integrations (human and otherwise). AGI engineers might be able to churn out fantastic code (some day at least), but we still need to work out the requirements and someone still needs to make decisions on how things are done. Decision making is often the worst/slowest thing in large orgs (especially public sector).