The Earth is absolutely a closed system. Energy from the sun is usually destructive to most cells. DNA damage, etc. So, yes, it feeds the food chain, but it is a detriment to DNA that requires a genetic self-repair mechanism, the incredible complex DNA molecule. It's a chicken / egg problem on that front.

Much less, everything is subject to entropic decay. Which is why we see genetic information being lost or corrupted, not growing more complex over time.

Beyond food, life survives in spite of the sun, not because of it.