Amazon can't undercut manufacturers (not without becoming a manufacturer). If they undercut middlemen who weren't adding any value, what do I care?

The middlemen are adding value by making niche items available on the marketplace. If they are gone the diversity of products will shrink.

But either Amazon will have the product or it will still be valuable to another middle man.

Amazon have a lot but are a long way off having everything. Health and Beauty for example, they may have the top 50k sales ranks pretty well covered but at least the top 100k are probably worth a middle mans time.

Not all products are really valuable to a middle man. From my insights regarding Amazon sellers, ~70% of the profit is made from ~5% of the products, and those are the products Amazon is taking away from them. If they then only have the low-profit items remaining, they aren't able to be profitably on Amazon anymore, unless they operate at significant scale - a scale that becomes very hard to grow to when Amazon is constantly taking away your means to do so.