I will suggest that the root problem in the public sector is to be found in the financial and data management.

In the public sector the value of services is assumed to be the cost of providing services.

Using costs as value indicator may be true to true transfer subsidies where the citizens has choice over use of funds such as pensions.

But the consequence is that effectivity is not measureble, ie. the capability of a sub-system to turn ressources into individual value to citizens.

Effectivity can be addressed as productivity (unit production costs) times quality (how well proces output meet individual needs).

Often quality in the public sector is estimate towards the political goal, but that is substituting overall system effectivity with means efficiency isolated of real consequences.

This is the root problem of all Command & Control Economic systems. Change processes lack governance as to economic performance and true value creation.

We have problem knowing if innovation (actual change) create or destroy value. And thus have problem learning and improving when choices are made.

We have three ways to deal with this
a) Privatization.
In politics that standard liberal approach is to privatize and reduce taxes accordingly. In the private sector competition and Price as as the coordination mechanisms capable of comparing and balancing a multitude of issues in complex systems.

However, as this as true redistribution and incentive effects, this is also a political discussion with deep and even ideological conflicts of interests.

Also there are a number of critical factors to take into account when privatization is considered. E.g. in public infrastructure, who is acting as the customer paying for reserve capacity, emergencies, longterm investments and maintenence ?

b) Best practice
Trying to compare the same subsystems accross borders assuming all things alike. This should be done nomatter what, but it does not provide a solution as it does not provide a mechanisms to drive innovation.

Three inherent problems of this approach
1) It is not one-dimensional issues. A lot of factors work together as a system providing different results. E.g. Healthcare where on country may be really good at preventive healthcare improving health of citizens, but if you compare e.g. Cancer treatment, you are comparing treatment of the worst patients in the best country with the average patient treatment in the worse country ending up defining the best solution as worst.
2) Best pratice assume someone make better solutions, but there is no driver as to continous improvemens and measure what is better solutions.
3) If you treat customers as average customers, you get average solutions which reduce quality of service. Worse - if you standardise output to average, then you actively kill the innovation process.

c) Empowerment
There is a third route which is more operational without the political implications, but should not be looked on as a magical quick-fix.

If you ensure citizens are in total control of data, then you can enforce an allignment of value chains to individual requirements and input. You can ensure that citizens technically CAN CHOOSE between true alternatives incl. multiple domestic providers, cross-border or even cross-sector.

We are talking control as in a services CANNOT get data elsewhere then from the citizen herself ! Not merely some hub solution based on massive centralisation with a "consent" for appearance. In such a pseudo-control system all processes will orient themselves after averages and Command & Control principles and consent merely being legitimization.

The effect of this depend on quality of implementation.

For instance, innovation and value creation could be imprioved, if the public sector economic performance measurement where altered to ensure money followed citizens choice and even better where actual price negition in the face of alternative can be established.

What is critical is to allign public sector value chains best possible with individual value assessment as the only way to get a value driven innovation.

The second best to actually measuring value is that citizens - given real alternatives - would choose the service.

Without Empowerment and real openness to offer and choose alternatives, the system will suffer from accumulating Command & Control ineffectiveness leading to one of two unacceptable consequences - higher taxes or constant erosion of quaility.