Are rain gutters necessary if the landscape drains properly?

I live in Southern California and will be redoing our wood shake roof with light concrete tile and was quoted a price of $5000 to replace the gutters (would need wider gutters due to new tiles etc, and house is approx 4000 sq ft with garage.) Currently we only have gutters on half the house since my previous contractor told me that the water would drain properly on those areas without them, and we also had installed many drains on concrete areas. In the past few yrs as the roof has deteriorated, I noticed the old gutters are not even attached to the roof anymore and the water spills thru the gaps. However, the water always seems to drain well enough into the drains. Also, our house has wide eaves that slope upward at the edge, so the gutters are very visible from the inside of the house. Read: ugly! I would like to avoid the looks and high cost if possible.