If you have Spiritual trait, religion has many benefits. That is why the AI's with Spiritual trait generally beeline the religion tech track to found a religion (or two!). They are my main competitors in nearly every game.
It increases your happiness cap in all cities that have state religion. We Spiritual leaders can build Temples faster than other civs, and that adds to the happiness cap.
The Shrine is good for culture, for gold, and for spreading the religion. Depending on the situation, I will sometimes uses one of my early Great Prophets to build it.
Then, when you get Organized Religion, you can build anything 25% faster. That is a huge advantage over civs that have no religion.
If you are good at diplomacy, you can use religion to create or avoid wars, or maintain alliances. That gives you better results in tech trading.
There's more, but these are the main benefits of religion. I have noticed that most people on this forum do not value religion. My theory is that most of them are warmongers. I agree. If warmongering is your game, you have more important priorities. But then, if you want to go that route, you should not choose a Spiritual leader in the first place!