Attach rate goes down late in a console's life as more and more of the install base represents repurchases, users who have moved on to newer consoles, low end customers who would only buy at a rock bottom price, etc.
However, for the first several years of a consoles lifetime, the attach rate should grow very quickly, as essentially the entire install base represents current, active users, willing to buy new software.
"[Our former customers] are unable to find software which they WANT to play."
"The way to solve this problem lies in how to communicate what kind of games [they CAN play]."
Satoru Iwata, Nintendo President. Only slightly paraphrased.