I don't know - it seems to be a no-win situation to me. The public's attitude in contradictory.
Have a big RF undertaking lots of duties and engagements -the the public are up in arms complaining about paying for all of these people to carry out events.
Have a smaller RF - then the public are up in arms complaining about why nobody is doing all of the Royal work.
Perhaps we need to define the scope of what the RF should do? Also possibly differentiate between the "figurehead" royal roles - for example patronages of organizations and charities that could be done be non fulltime working royals and the key projects that require longterm inputs.
William should talk to his Scandi counterparts about how they have coped with their younger siblings removed from ongoing royal roles - it's happened in Denmark and Sweden in the last 5 years
I think one of the biggest problems is the invisible work they do that is not immediately obvious to people. It's the same with any job that doesn't only involve straight up physical labour, there will always be people complaining that unless they see a shovel moving, that person is not really working at all.
Most negative comments under any news story about the royals are about them doing nothing but cutting ribbons and eating free lunches wearing designer clothes. Even if we're not talking about royals per se, desk jobs and mental labour are not valued by some people. They also do not see how tiring in reality it is to attend events in formal wear, having to remember everyone's names, background, engage in conversation, look interested no matter what you are presented with, working to advance the issue you are promoting in that event, going from place A to B, then to C and D. It doesn't matter whether your arse is parked inside a luxury car or you're flying somewhere in business class, it's still not fun, it's work. You're tired, your legs and back ache, it's exhausting even if it's not the same as physical labour. And then that's only one part of it. People think royals have staff to do everything for them but if you are not a Harry but more like an Anne, you do the hours yourself and don't just rely on being quickly briefed while hurrying to some event. I'd love to see any of the complainers for example read all the boring documents Charles has to read at 2 am to be informed of all that goes on in the country and aware of the current legislation.
So, what they would have to do is make people see what it is that they actually do and how it makes a difference in people's lives. You can say royals have no place in modern society but then again, no tourist is going to visit a republic just to see a presidential palace and perhaps the parliament. Royals do have a place in supporting charities, working as a uniting figureheads that offer stability over long term without political leanings. I've also noticed the quality standards for many things are higher in monarchies compared to republics for historical reasons. Craftspeople for example had to strive to acquire royal warrant of appointment and you did not get there with shoddy work. This quality issue and the continuing traditions can be seen very clearly for example when talking about restoration of historical buildings; years ago I was living in a republic and they were renovating an old building. It didn't work out because "we just don't have the knowhow in this country for repairing this kind of thing" and a specialist had to be flown in from a country that still has a royal court. This all coming from someone who has observed the differences for decades having lived in both kinds of countries, monarchies and republics.
As long as people see royals as only useless handshakers cutting ribbons, they will want to get rid of them. I think Prince Philip had the right idea. I don't think I ever knew how much he influenced things until he passed away and I learned a lot more about the Duke of Edinburgh's Award and his work with environmental issues. Sorry for the long post, hope this makes sense at all!
