Firstly IMO your lack of water clarity is not caused MAINLY by water blooms. Koi are making or roiling the water to be murky and the bottom aeration mixing is helping a lot to keep the resuspended very tiny (0.3 to 3um) bottom dirt in suspension. Turn off the aeration for 3 to 6 weeks and watch how much more clear the water very gradually becomes; maybe close to 2-3 ft IF and IF you have no more than 2-4 koi in 1/4ac. Use a secchi disk to measure the water clarity for measurements and comparisons. See next.

With several or numerous koi in a 1/4 ac pond or any pond IMO and experience that does not have extremely large mechanical filtration the water will never be any more clear than around 3ft often it will be less of 6"-12" when the water is above 60F. The more koi present the muddier the water becomes. Your pond water is very likely relatively clear when the ice melts in Spring. This is because the koi are have been relatively dormant all late fall and winter with very little feeding activity when the water temperature drops below 45F and they do very little feeding due to cold water and their cold body temperature. Ice cover with no wind action nor carp feeding allows the suspended sediments to gradually settle toward the bottom. Thus when the ice melts the water is clearest of all year. As soon as the water warms and koi become actively feeding the water becomes more and more turbid. Watch for this to happen each Spring.

Realize that koi have exactly the same body features and anatomy as a river carp. I call koi aquatic rototillers and aquatic pigs. The Japanese worked with european and oriental carp (Cyprinus carpio) a few thousand years ago and selectively breed them to have all types of color with various body patterns . In reality,,, some of the offspring of Koi are drab color and have identical body color of river carp because their genealogy is river carp. Same drab color thing happens when breeding goldfish. Goldfish are NOT koi; the two are different species. River carp have a suction type protrusable mouth that they use to dig 1"-3" deep into the sediments searching for food items that live in and on the sediments. Their feeding activity stirs and roils the bottom sediments thus creating murky, muddy water behind them as they feed. Koi do not have stomachs, just intestines, thus they cannot binge feed thus they feed frequently and hourly searching the bottom sediments for food. This frequent feeding activity roils the bottom sediments. If the pond has aeration, the circulation activity of the aerator helps keep the very tiny resuspended sediments in suspension making or keeping the water even more turbid. Try not running the aerator and see and measure (secchi disk) what happens to water clarity.

IMO the good thing about koi is their bottom rooting and feeding activities helps aerate and mix the bottom sediments. The fewer koi / carp that you have in the pond the clearer the water will be. I have proven this many times. Clear koi ponds have lots and lots of mechanical water filtration to minimize all the muddy conditions crated by koi. Many of the clear (4-7ft clarity) koi ponds that you see have little to no mud /clay sediment in the bottom and have extensive mechanical filtration. .

Back to your original question - alum is aluminum sulfate. Each alum treatment for making the 3 ft of clarity will be VERY temporary due to actively feeding koi. Aluminum is a heavy metal and does accumulate in the bottom sediments with each usage. Heavy metals do not decompose nor rot up. Too much heavy metal even aluminum when used too frequently can later be an ecological toxic problem.

The good news is your pond does not have weed and algae problems because the murky water from the koi activity keeps sunlight penetration to a minimum so plants don't get enough light to grow well.