Get feature values from ImageCollection to list

I am calculating the mean precipitation value over a given area from CHIRPS precipitation data.
My goal is to get a list containing a date and precipitation value for every Image of the ImageCollection.

Using .getInfo() on the reduced ImageCollection I can get a dict representing the ImageCollection and from there select the values on the client side.

import ee
from datetime import datetime

ee.Initialize()

dataset = ee.ImageCollection('UCSB-CHG/CHIRPS/DAILY').filter(ee.Filter.date('2016-01-01','2016-12-31'))
area = ee.Geometry.Polygon([[[29.045341997822412, -2.1339228457039368],
                                               [29.07984593458999, -2.1339228457039368],
                                               [29.07984593458999, -2.0966977113182073],
                                               [29.045341997822412, -2.0966977113182073],
                                               [29.045341997822412, -2.1339228457039368]]])

 # Image reduction applied to each image.
def reduce_dataset_region(image):
    # Calculate mean of precipitation on defined area.
    local_precipitation_image = image.reduceRegion(
        reducer=ee.Reducer.mean(),
        geometry=area,
        scale=20
    )

    return image.set('mean', local_precipitation_image)

# Apply region reduction to ImageCollection
reduced_dataset = dataset.map(reduce_dataset_region, True)

# Request server-side ImageCollection as dict
reduced_dataset_dict = reduced_dataset.getInfo()

# Create list to hold daily precipitation values.
precipitation_list = []

# Loop through features in image collection dict. One feature represents one image.
for feature in reduced_dataset_dict['features']:
    # Get date and turn into datetime
    # Get precipitation value and add with datetime to list.
    precipitation_list.append((timestamp, feature['properties']['mean']['precipitation']))

print(precipitation_list)

This seems slow and not the right way to go, especially since I want to use data from multiple years.

How can I create a list containing the precipitation value for each Image and send only that, and not the whole ImageCollection, to the client? What is the better alternative to .getInfo here?

import ee

ee.Initialize()

dataset = ee.ImageCollection('UCSB-CHG/CHIRPS/DAILY').filter(ee.Filter.date('2016-01-01', '2016-12-31'))
area = ee.Geometry.Polygon([[[29.045341997822412, -2.1339228457039368],
                                               [29.07984593458999, -2.1339228457039368],
                                               [29.07984593458999, -2.0966977113182073],
                                               [29.045341997822412, -2.0966977113182073],
                                               [29.045341997822412, -2.1339228457039368]]])

# Create list to hold precipitation values
precipitation_list = ee.List([])

 # Image reduction applied to each image.
def reduce_dataset_region(image, list):
    # Calculate mean of precipitation on defined area.
    local_precipitation_image = image.reduceRegion(
        reducer=ee.Reducer.mean(),
        geometry=area,
        scale=20
    )

    return ee.List(list).add(local_precipitation_image)

# Apply region reduction to ImageCollection and return result in List
reduced_dataset = dataset.iterate(reduce_dataset_region, precipitation_list)

# Request server-side List  as dict
reduced_dataset_dict = reduced_dataset.getInfo()