The Prince of Wales is currently in New York to promote his Earthshot Prize, which aims to celebrate and scale-up solutions to “repair” the planet.
And while the Yahoo News survey's results show the vast majority of people (71%) think Kate is doing a good job in the role – compared with just 12% who feel she is doing a bad job – her popularity is less fixed among younger respondents.
Our results come shortly after a YouGov poll showed 26% of Brits think the UK should have an elected head of state – the highest since at least 2011.
While 80% of the over-65s said that Britain should continue to have a monarchy, this falls with each age group to just 37% of 18-24 year olds and highlights the challenge facing the Royal Family of staying relevant with all sections of society.
How good a job is Kate doing?
Polling for Yahoo News from Savanta shows that, overall, 71% of people think the Princess of Wales is doing a good job, while 12% believe she is doing a bad job.
Of the 71% who rated her performance positively, 41% felt she was doing a very good job, and 31% said she was doing a 'somewhat good' job.
But older people tend to see Kate more favourably than younger people, with 82% of over-65s saying Kate was doing a good compared with just 49% of 18-24 year olds – with whom the monarchy as a whole is less popular.
Graham Smith, from anti-monarchy campaign group Republic, told Yahoo News: "This doesn’t surprise me. The idea Kate was going to help save the monarchy was always fanciful.
"Younger people are increasingly disinterested in the royals, seeing them as a symptom of a society that is unequal and which favours the rich and powerful. Kate is just more of the same and only attracts the interest of people already keen on the monarchy."
Meanwhile, regionally, people in London were the least likely to think the Princess of Wales was doing a good job (62%), while those in the North East were more most likely to view her performance favourably (83%).
Should William open up palaces to homeless people?
Savanta's poll also asked respondents whether Prince William should make the royal palaces available to homeless people – with the majority believing he should open up the buildings.
In June, the Prince of Wales announced his project Homewards would aim to show it is possible to eradicate homelessness. The project, part of William's extensive charity work, will work in six towns and attempt to find local solutions to the issue of housing.
Polling shows 52% of people would back William opening up royal palaces to those experiencing homelessness, with 22% opposing the move. Of those who backed it, 26% said they were strongly in favour.
The idea was most popular with people in the 24-35 age bracket, with 65% saying they thought it was a good plan.
There was a marked age difference in those who "strongly opposed" such an idea, with only 7% of 18-24-year-olds very much against the notion, compared to 44% of 55-64-year-olds.
Where should George go to school?
The eldest child of William and Kate, and future king, is currently being educated at the private Lambrook School in Berkshire, alongside his younger siblings Charlotte and Louis.
It is thought that he is likely to follow in his father's footsteps and attend Prince William's alma mater Eton when he turns 13. There has a suggestion by a Labour MP earlier this year that the youngster should attend a state school.
Despite fees for Eton hitting more than £46,000 and the country being in the midst of a cost-of-living crisis, Yahoo's polling showed people were divided on whether the future king should be educated.
Just 35% of people felt George should attend a state school, while 41% said they thought he should be educated at a fee-paying school like Eton, and 25% said they didn't know.
Views, once again, varied with age with 46% of 18-24-year-olds believing George should attend a state school, compared to 27% of over-65s.