Now that I think about this some more, I'm not thinking that this is a way to limit the number of bags on the train. I'm thinking that the extra fees, the reduction in number of bags, and the change to a 45 minute cutoff is a way to limit what's required of station agents. Between these changes and the switch to e-ticketing, Amtrak can conceivably reach a tipping point in certain stations where they can go from 4 agents down to 3, or from 3 down to 2, or from 2 agents down to a single agent on duty.
In almost any business, your labor is your greatest cost, and I'm betting that the primary reasoning behind this is as one part of an effort to reduce labor costs.