There are several things to consider in answering your question.
An objective answer to your question would require a direct comparison between the total usage of
後で at two different points in time. This is not a trivial task and it requires more specific information, i.e. exactly which two time points to compare, what corpora you will base your conclusions on, whether you want to include
Nounの後で or other variants as well, etc. You could then see if there is a pattern of attrition and perhaps even investigate the reasons.
If you are just looking for a subjective answer, then it is reasonable to ask native speakers but I think you would also have to use example sentences generated by native speakers. For example you could take 20 sentences containing
後で from a corpus and show them to Japanese people to ask whether they feel something is unnatural in the sentence. The reason I believe it is important to avoid non-native speaker examples is that they often have errors which can make the sentence sound unnatural for a variety of reasons that might not be immediately apparent, even to native speaker.
Take your sample sentence, for example.
According to the Dictionary of Basic Japanese Grammar,
後で indicates "any space of time after" whereas
～てから indicates "the space of time following after". It may well be the case that
would sound more natural to a native speaker precisely because of the implication that the action of going home immediately followed the action of watching the movie, and was not separated by "any space of time". So you could argue that
後で is not the appropriate term to use in this specific circumstance because of the meaning of the sentence. You have to be careful attributing a cause to an effect and so I think it is best to avoid sentences made by non native speakers.
Finally, when something does end up becoming obsolete there is usually a reason for it, and it's often the case that it is superseded by something else. You might investigate which terms are more likely to be used instead of
後で as another way to explore your question.
So without directly answering your question, I hope that helped. :)