Then I thought about it. I realized this was an opportunity rather than an inconvenience. I can save energy costs! I was inspired some time ago by the Fort Collins net-zero electric energy home, and maybe this is one of many steps I could take to reduce my energy consumption at home.
I did the calculations (see comments for my actual calculations) and found that I will be saving $68.58 per year on energy costs by having a manual garage door opener in place of an electric one.
I was speaking with a coworker about this very calculation, and she pointed out that the marginal utility of having an electric garage door opener versus a manually-opened garage door is highly in favor of the electric opener, given the cost savings. For some people, spending $5.71 per month to have an electric garage door opener is worth the cost. For myself, it's not; we only park the bikes in there, not the car, and don't use the remotes -- just open it from the inside anyway.
For now, I'm happy with the arrangement. The cost savings is definitely worth the marginal utility loss.