Every cloud has a silver lining. Being unable to travel at the moment, I have extra time for trip planning. In researching points of tourist interest in Helsinki and their cost, I noticed that one of the museums was free not only with the Helsinki Card (which is the typical sort of day-limited deal) but also with something called the "Museum Card"--and I actually took the time to follow that lead. It turns out that the Museum Card is not limited to sights in Helsinki, is good for a full year and costs only €69.
By comparison, a 3-day Mobile Helsinki Card (with no transportation benefits) costs €59. The Helsinki Card covers a lot of non-museum attractions and might be worthwhile for others who tend to go more places and spend less time at each one, but I am not interested in things like bus tours, and I couldn't possibly get through museums fast enough to get value from that deal. Nor do I want to contort my sightseeing schedule in order to cram all the covered sights into a 3-day period; I want to organize things geographically and have the freedom to wander if I see something interesting.
The Museum Card is structured for people like me. It covers an advertised 300 museums and allows a full year to see them. Most of the listed places are true museums in the sense that they have "Museum" in their names, but there are some other types of attractions included, such as Helsinki's Rock Church and LOUMOS Kaisaniemi Botanic Garden. The card covers the entire country, including places I'm interested in that are located in Espoo, Turku, etc.
Not absolutely every museum on my target list is covered, but I see about €90 worth of sights I want to see in Helsinki and Espoo alone. Since the card isn't limited to just a few days, I don't have to worry about what I'll actually be able to accomplish during its period of validity.
Reminder: Anyone who might qualify for senior discounts should check attractions' websites for accurate pricing before making a final decision about any sightseeing card. It looks like €2 is a fairly common discount for seniors in Finland, and that's a modest amount, but I've run into substantial senior reductions in some other countries.