I'm very much ok eating solo in fast food and sit down restaurants thanks to a few years of living solo far away from home after college. Disney would be no exception (I've done it at
Disneyland).
However, V&A's is probably one of the few restaurants I would not do solo. (Monorail Dine Around and Dessert Parties also come to mind.). This experience is an EVENT. one you'll want to talk about for years to come. It's so great to be able to share that with my wife. It's so expensive that I wouldn't want to sit there buried in my phone like I'd be comfortable doing solo at a normal restaurant, and there's no chance of real conversation with other diners.
That said, it was definitely worth it for us, and I think you should convince someone else in your party to join you!