Look at algae this way Blackmaler it consistes of millions of in "laymans terms", of tiny plants that act as one to produce oxygen during the daylight hours, but at night though this self same millions of tiny plants start to rob the pond of oxygen because they go into reverse and produce Co2 insrtead of O2.
So yes algea can be good for koi but we prefare not to have it in our ponds turning our water green for that reason, which if not watched can cause catastrophic Oxygen Deoeteion of your pond killing all of your koi, so we keep our pond we aireated,by a spindrifeter bottom drain bubbler plus oxygenate all our filters , we also try to keep nutrients at a minimum as they can cause the algae to bloom, so feed only as much as they will eat in 5 minutes
So too much algae in our veiw is bad for your koi in our veiw and you should set about removing it soonest, try using quilt batting
The other obvious reason is that if your pond is green then you cant see your koi at all so why not get rid of it ?
In saying that though we do have algae in our pond that grows on the sides and bottom of our pond.
We koi keepers have a trick or too up our sleaves if we do get a green pond, there is a company called TAP who produce anti algae pads , it has a unique 4 way action on your pond i enviromental, Mechanical Chemical and biological and will clear your pond of algae in about 4 days if you place one or two depending on the gallonage in your filters it has now been improved with a new formulation.
I had a read of one at the fish shop the other day , they had them on display by the till, or as you guys like to say a cash machine counter and the new improved forumulatioon bit caught my eye so I picked it up and read it , I'd had cause to use one when we first started in the pond and they reallly do work so either google them to see if you can get them online or ask at your local fish outlet they may well do them in the US.
Dave