It's easy to over-think design. The hilariously overwrought and over-intellectualized b***sh*t that was revealed when the new Pepsi logo went public (great article and the actual document here) gave rise to much rofling, deservedly so. It's a fine example of the "baloney baffles brains" approach to design. It produced a monstrosity, and I was not in the least surprised by the recent announcement that Pepsi's market share had fallen to #3, below Diet Coke. (A brilliant parody on the consequences of over-thinking design here.)
The sun, the source of energy, light and life for (almost) all living things on Earth, worshipped as a god throughout history, featured in religious art of all kinds since prehistoric times, is an evocative symbol. Well, surprise, surprise. This needs neither analysis nor explanation and, in my not-in-the-least-humble opinion, is much better without either one. Far from being trendy, the sun is (from a human perspective, anyway) completely timeless. Methods of depiction change from time to time and culture to culture, but the basic symbol retains its associations regardless. Ditto water, sky, greenery, mountains, fire and a host of other evocative images and their derivatives.
Within individual cultures, there are other symbologies with similarly deep roots and inevitable connotations. Digging for deep psychological, biological or metaphysical reasons for this is about as useful as psychoanalyzing Hamlet: it might be interesting, in a vague way, but it won't help a working professional create a more effective product.
Over the centuries, different schools of art or design or music evolve out of the technologies and cultural interactions of their day. They start out as innovation, become trends, go out of fashion, then become classic styles that can be evoked ever after by generations of artists. But the intellectualization (sorry for the polysyllable) of those techniques has never of itself produced great art or great design in any era.
Da Vinci and Michelangelo took deep dives into anatomy, mathematics and classical Greek art to redefine painting and sculpture. They produced work that is as breathtaking today as it was when it was new, but they were artists who knew, first and foremost, how to communicate. Their theories and techniques, in the hands of imitators who knew only the theory and not why it was there, produced dull stuff, only mildly interesting for all that they hewed to the right proportions, the proper sfumato and chiaroscuro.
As Jin very correctly points out, the fact that a given symbol is in use on a site (if it's well designed) is an indication that it is appropriate for the message.
The message, in design, is everything. Keep it in mind, and keep it simple. Over-think at your peril.