The bland problem usually isn't the soup itself - it's that cold dulls flavor perception, so you actually need to oversalt and over-acid compared to what feels right at room temperature. I'd push back on holding off the acid until serving though; that works for some things, but gazpacho genuinely needs a day to meld, so mix it all in and just taste it before eating to adjust. The real durability issue is separation and sogginess, which you dodge by keeping chunky elements separate (croutons, diced cucumber, avocado) until you're ready to eat, then just stirring them in rather than blending everything into mush.
Vichyssoise (potato-leek) and cold beet soup both hold up better texture-wise because the starches and natural thickness stay stable, whereas tomato-based soups can get watery. If you're tired of the vegetable-forward route, cold avocado or cucumber soups with proper stock (chicken or vegetable, not water) and seasoning hit completely different - they're richer and actually feel satisfying on a hot day rather than like you're drinking lawn clippings.