For better or for worse, I like the consistency of the Royal Family. Fashions / celebrities come and go, shiny politcians come in full off promises and quickly tarnish, the media is full of "Crisis" and catastrophe, but the Royal Family is there even with their own dramas which tend not to affect us that heavily.
I think their continued existance adds value to their tourist assets. The Crown Jewels are real, used ceremonial items, not just preserved, historic, museum pieces. It is a bit of a USP compared to other countries that are republics or heavily toned down monarchies.
Personally the Duke of Edinburgh's award has had a long term enrichment on my life. Other charitable foundations like The Prince's Trust also benefit society, or royal patronage does boost support/ publicity for charaties/ good causes/ issues particularly if they're not particularly trendy at that moment (e.g. Prince Charles having an early interest in environmental issues)
The Queen Mother said hello to me at a public event where the royals are regulars. Princess Anne opened a refurbished public services building in my home town as a child which was a bit of glamour.
We've got expensive assets to maintain anyway, and an additional President would have multi-million pound costs anyway.
I think the Royals add some USP to the UK and some feel good factor. At occasions like Jubilees/ major weddings, it does enourage community spirit.
The move to a smaller core of working royals is good and more likely to keep peripheral members of the family out of embarassing issues.