It's in good condition- we wouldn't have to do any updating in the next 5-10 years

Probably talking about a lot more expense and bother renovating a house than having to do some clearing - depending on how many unwanted trees they might be and how big they are.

When trees are big enough and of locally desired kinds you can have a logging company cut them and clean up afterward, split what the mill pays for them with you.

They're dense enough to be nearly impenetrable for an adult in the summer on 2/3 of the property. They're all 10-15 feet high, I didn't see any branches that looked like they had a diameter larger than 4ish inches. The neighbors have them also- they grow wild all around here (southcentral AK).

I'm worried that given the invasive nature of alders I'd be stuck with a major clearing project every year and not get to do much of growing plants that I do want.

Even as fast as alders grow you should still have plenty of time to cut, mow, pull or spray replacement seedlings before they are also 10 ft. tall.

Alders are omnipresent in my area as well :-) But they are one of the easiest of our native trees to clear and keep out of a cultivated garden. They generally grow pretty fast but without a significant trunk diameter so not too much of a chore for a homeowner with a good chain saw to cut back. But you will have to deal with stump removal.

Alders are a pioneer species - they tend to rapidly colonize land that has been cleared or logged but left open/unplanted. Once the area is cleared and replanted with the ornamentals of your choice, reseeding of the alders is far less of an issue - seedlings are easily removed with any other weeds.