The main problem I see with that explanation is that no other animal "evolved" any kind of behavior that could reasonably be termed "religious". No animal has ever been observed in what could be described as prayer or worship.
To get organised religion, one would need language/communication. Animals might have some sort of spirituality or religion, but absent the level of language needed to make organised religion it would have to be on the level of personal belief. So how would one detect if an animal has some sort of personal belief or not? Keep in mind that prayer and worship are human expressions of religious belief. If an animal has some sort of religious feeling or belief in a larger power outside itself, how would it show this and how would we recognize it? I think you are asking for something that would be very hard to detect. Even if we detect it, it would be inconclusive and open to interpretation.
I am reminded that elephants show behaviour that looks suspiciously like mourning their dead. If this can be taken as a display of religious belief or not is obviously a question of interpretation.
Everything than humans do, animals have also been observed doing, of course on a vastly lower level. If you can name any other activity that man does, that is not at all found to some degree in some animals, please do so.
Humans have an abundance of language, culture, dance, creative expression in many forms, the capability of abstract thought, high self-awareness. While you also can find some of this to a small degree in animals, I believe there is a threshold one has to get above before one sees behaviour that we humans would recognize as some sort of organised religious belief.
Nobody has ever explained to me how the "wasting" of resources and energy on religious activity, collectively or individually, makes humans more "fit" to survive. If anything, NOT spending time and effort building cathedrals, churches, synagogues and mosques, as well as engaging in other religious trappings, such as embarking on long weary, dangerous pilgrimages to distant places, should be an evolutionary advantage to those groups and individuals who avoid all that.
Building expensive places of worship and going on hazardous pilgrimages is a very recent thing, on an evolutionary scale. You are talking about fairly recent displays of worship; and displays of surplus at that. More common human displays of worship and spirituality on an evolutionary relevant scale would be things like cave paintings and covering a dead tribal elder with flowers and putting a walking stick in his grave to aid him on the journey in the afterlife.
When it comes to what advantages religion would have for early man, there is lots.
Remember that most religions in those days (from what we can gather from what artefacts they left behind, and of what can be learned from isolated tribes today) were animist. As such, they attribute a "soul" or some sort of intelligence or purpose to plants, animals and natural phenomena. In short, nature becomes a person/force/deity that the human mind can attribute cause and will to. Apply some lore and an oral tradition, and you have a framework where tribes of early man can gather and remember information that is important for survival. ("When the god in the sky turn the heavens grey and the daughters of Ibis take to their wings and fly to their father Mountain, then we must travel down to the river. Ibis is alone from watching eyes, so this is when Antelope will bring his children to visit her. We will wait for them at the ford")
In short, religion fill the needs for group cohesion, enforcement of mores and collection of information useful for survival. We see lots of evidence for this even in "modern" religion; the Bible and other religious texts from the same era has a fairly small volume of text spent on genesis or creation but has pages upon pages of social mores, rules, laws and histories.
Man alone has been given a unique ability and yearning to communicate with his Creator. That is why there never has been and never will be a culture or tribe that is not religious. Even those who deny the existence of God, eagerly spend billions in programs such as SETI
Man has a yearning to understand the world. If we had no desire to understand the world, we would likely have gone extinct. The early explanations we made for how the world works were attributed to gods or the supernatural.
