I think you're absolutely right there: constant immersion is needed to provide the context for learning. My mistake was that I wasn't reading enough Japanese to make use of the memorised characters from Anki, so they were quickly forgotten.
There still remains the problem of review card creep, though. After adding about 5 new cards a day for a year and reviewing them every day, I ended up having to review hundreds of cards a day. Your suggestion might fix this too, though, now I think about it. If I'm using the memorised information outside of Anki (by reading Japanese articles, etc), I'll remember them better, leading to less reviews of those cards in the future.
There still remains the problem of review card creep, though. After adding about 5 new cards a day for a year and reviewing them every day, I ended up having to review hundreds of cards a day. Your suggestion might fix this too, though, now I think about it. If I'm using the memorised information outside of Anki (by reading Japanese articles, etc), I'll remember them better, leading to less reviews of those cards in the future.