I used to treat algaecide like a required step too, mostly because a lot of closing guides bundle it into the process. After a few seasons I realized the bigger factor was always the condition of the water when the cover went on.
The year I had the worst spring opening was actually when I did use algaecide, but I closed a little early while the water was still warm and there were leaves breaking down in the pool. By spring the water had that dull green tint and the filter pressure climbed fast once I started circulating again. Ever since then I’ve focused more on getting the pool really clean before closing, running the pump long enough that the filter grabs the last bits of debris, and making sure the balance is steady before shutting things down.
Now I usually wait until the water temperature drops quite a bit before closing. Cold water slows algae growth so much that it becomes less of a factor over winter. If the pool is clear, the organics are removed, and circulation has been good before the cover goes on, that seems to matter more than whether an extra bottle goes in at the end.
That said, I can see why some people still use it as insurance, especially if they have to close while the water is still relatively warm or if their cover lets in more light. For me the biggest difference has always been starting winter with really clean water and normal filter pressure rather than relying on extra additives. Anyone else notice the spring opening is easier when the pool is closed later in the season?