Why compost?

Before comming to the peruvian Amazon jungle i was composting but here The locals tend to throw organic garbage directly on The soil near The plants. I was wondering which benefits are in creating compost with The organic garbage instead of directly throwing organic garbage to The soil?

One advantage i was thinking is that composting would neutralize The allelopathetic property of some leaves that inhibit The grow of some plants. But which other benefits You see besides of this?

If i don't use allelopathetic plants is there is a benefits composting? Or should i throw My organic garage directly to the soil?

Cheers

R.

There are multiple potential benefits to composting.  That said, tossing organic material near your plants isn't necessarily wrong.  It is a matter of whether you want/need what composting offers:

Composting allows you to collect organic matter into a specific location.  This allows you to keep your growing areas cleaner and prettier.

Hot composting can help kill pathogens and reduce the spread of diseases.

Composting allows for better mixing of raw inputs that results in a more nutrient-balanced output for your garden.

In temperate environments, hot composting helps materials to break down far better in fall/winter.

In your more tropical environment, insects, fungus and bacteria will be able to break down the organic matter any time.  If you aren't worried about keeping the garden area more organized/pretty, aren't worried about using composting to break down the materials faster and aren't throwing diseased plant matter near similar growing plants, then it may be perfectly reasonable to throw such matter on the ground near your plants.  They will break down and provide nutrients back into the soil and feed the local biome in the same way that other natural plant detritus will.  In addition, the fresh organic matter can act as ground cover to help retain moisture and reduce weeds.  

A final benefit is that using the raw organic matter avoids the additional labor and potential expense involved with composting.

A couple of other benefits of composting:
Potential for reduced odors, depending on what you are composting and in what quantities.
Less chance of attracting nuisance insects, animals, birds to your gardens, or worse -- into your home. Or items being taken away to neighbor's yards who might not be happy about this. Especially if you want to include meat/fish/bones/dairy...
Ability to utilize shredded paper or cardboard without troubles with the wind blowing it away.
Hot composting bio-plastics at home.

I suspect it depends on where you are and how does soil build up naturally where you live.

For example, a lot of places, the soil builds by leaves and plant matter falling then decomposing.  Fruits, foods, etc, would pass through an animal before adding to the mulch.  If you live in a place where this happens fairly quickly, without smells, and without scavengers like rats, birds, and more vicious creatures, then go for it.  

But like nature, there are loads of different ways we can build soil.  Where I live it's either too dry or too cold for the leaf litter to compost on top of the soil, so it either crumbles into a dust during the summer, or it has to wait a year and a half for the next layer of leaves to trap in the moisture before it starts decomposing.  We also have a lot of rats and other animals that love scavenging off human food scraps, so we pre-compost or trench compost (nature has to dig as part of soil building in some places too - like animals burying food then forgetting about it) because it's easier to prevent rats than to get rid of them.  

Then there are half-way methods like layering the scraps under mulch.

If you have any disease, (or potential like tomatoes or potatoes), pests, or things you don't want to seed, then heat composting is a good idea.  

Lots of choices.  Try as many as you can and see which work for you.

I live in a relatively dry climate that is frozen solid for 5 months of the year.

If I didn't compost in large piles or containers, I could never retain enough moisture for decomposition. Even then, complete composting is a multi-year process.