That is interesting and I have a similar situation here with paint. A few years ago I had a company paint my garage roof. It was in good condition just a little dull white. They used expensive Sherwin Williams products and in less than a year roof looks like it does now! The metal edges are even rusty (I'd have to get ladder & show from above). I had them paint walk-in door frames which you see are rotting.
Maybe something to do with paint today vs what they used years ago.(?).
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I'm sorry that the paint job has not held up the way that one would expect.
If it were me, I would be having a discussion with the painters. Paint preparation is 90% of the job in my experience. I painted to put myself through school, and have always been interested in paint chemistry and coatings.
Sadly, I think that if it were me, I would be replacing your door trim at this point, and hoping that the door frame can be repaired. There are "Dry-rot" epoxies to solidify rotted wood, but if the water is getting in higher up, that won't help. Is there standing water at the door when it rains? As to the algae, I use "Wet-n-Forget". I would try that on your roof to see if it improves things. If it doesn't, I tend to reach for more potent cleaners. Was this an issue before it was painted as well? E.g. a north slope that never gets sunshine?
Take the following with a grain of salt as they say. I'm a Sherwin-Williams advocate, based on decades of experience with their paint and others. I do use other brands. We currently have Sherwin-Williams paint on the house and outbuildings and 90% off it is in good condition 19 years later. The material that isn't 100% is on surfaces where the underlying material is failing, or has failed, so not really the fault of the top layer. (Think 100 year old paint on 100+ year old wood that was repainted 19 years ago with a new layer.) Preparation is 90%...
However, Sherwin-Williams makes an enormous range of paint and paint quality. Here the low end paint is in the $35/gal price range, and the high end residential paint is in the $140/gal range. I believe that the high end paint is better. Is it 4X better? That's a tough call. I might use it on a house that I plan to be in for twenty years. Perhaps not if I only need the paint to last three years. I might use the pricier paint on areas that had access issues, e.g. multistory building, where the labor and equipment cost to get painters up in the air adds to the job cost. Commercial quality paints for special applications can be even more expensive.
However, great paint on an inadequately prepared surface is just wasting money and resources. Even a great paint needs a clean, strong, intact surface to adhere to. Sometimes, that is sanding, priming, second coat of primer, and a top coat or multiple top coats. If I am spraying, I always back roll with a roller to get the top coat into all the crevices. I think of spraying as a way to get paint onto a surface and rolling or brushing the paint as a way to get the paint into the surface. I never just spray latex paints, but that's just my personal opinion. I am more in the do it once and forget it category.
Sherwin-Williams makes a line of paint that is "self-cleaning" exterior paint called "Rain refresh" because the paint generates a cleaner from sunlight and water that dissolves off dirt sticking to the paint. ($$$, $130/gal locally) Obviously, it works better in areas that get rain periodically, and rather unusually it has a UV protecting agent that doesn't break down in sunlight. Those two items have benefits to an owner, and some geeky chemistry behind it.
All the best,
Peter
