Best way to politely remove someone from paper authorship who planned to contribute but did not?
Removing people late in the preparation stage of a manuscript is always prone to bad feelings. It is of course unfortunate that this is a fact. This is why it is always a good idea to try to set up some ground rules for authorship (or contributorship). There are many posts under the authorship tag that discusses the Vancouver Protocol which is a set of rules under which authorship/contributorship is determined. I usually provide the link to ICMJE as an example. The basic idea is that to be listed as author you need to fulfil certain criteria. Some have even devised a point system to calculate if a person is worthy of authorship/contributorship.

But, to answer the question when you face the fact. There is no easy answer. You could decide to be strict and simply state that no sufficient contribution has been made (quoting the Vancouver Protocol list). How badly this is received is something only you can evaluate. And, only you can assess if you think it is worth it if the consequences are in some way "high cost". You can also decide to let this one slip through and make sure you have a clear arrangement around the next manuscript you write. I also think it is a good idea to start introducing ideas around authorship/contributorship in your research environment. I am sure many will dislike the topic but you are on safe grounds. Remember, many, maybe I should say more and more, journals request lists of contributorship and provide a basis for evaluating them (usually following the Vancouver Protocol list)