Bike lockers are a popular, cost-effective method for secure bike-parking at transit stations. So what does the Amtrak’s ‘Station Program and Planning’ policy say about them?
Where market analysis or community funded participation shows that station usage warrants the inclusion of bike racks, the racks are to be located outside, in close proximity to the station. Signage should clearly indicate that Amtrak is not responsible for loss, damage or theft. The racks should be canopied, if possible, to afford protection from the weather. Due to security issues, the use of lockers is discouraged.

Based on context, don’t you think they just mean bike security? As in, the bike is not entirely secure and may be stolen or vandalized?
I was about to say it still doesn’t make sense to actively discourage them, especially over the alternative means of bike storage (out in the open attached to a chain/u-lock, but perhaps the distance and time spent away on a trip involving Amtrak could explain why they want to discourage people from leaving bikes there for extended periods of time.