I get being surprised, but upset and horrified is a bit much.
The only people IRL that I've heard say anything against double-barrelled - even really long ones - was a few much older people who associated with it posh money-grabbing types (the idea that they needed to show their full lineage), so the association here with chavs is an interesting contrast.
I didn't "give up" my birth certificate surname - that's not really legally possible, even with a name change, all previous names are legally connected to the person. My husband and I discussed a range of family surnames and we both chose one to go forward and share together as our community names (we both use other names for other purposes).
I also changed all my forenames, which wasn't giving up on all my dreams, but the culmination of a childhood dream as the names on my birth certificate were all begrudgingly given.
Why does a culture need a system?
Because humans make systems, and by definition, culture includes what humans create including all the social systems and customs like naming customs within the groups involved.
These systems are bound to change - centuries back, most people didn't have surnames at all, and even now there are cultures that don't, some which are being pushed to do so in order to standardise passports and similar. There have been similar issues when cultures have had systems where names are added or changed over a lifetime at life events, but there is international pressure for names to be standardise at birth registration. A little over a century ago, most people in the UK didn't have titles, most women didn't have to concern themselves with which cut up version of Mistress to use, now it's practically impossible to not use a title & there are all sorts of associations with each version.