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There is a paper on this historical/educational topic: Galili and Tseitlin, "Newton's First Law: Text, Translations, Interpretations and Physics Education," Science & Education Volume 12, Number 1, 45-73, DOI: 10.1023/A:1022632600805. I had access to it at one time, and it seemed very relevant. Unfortunately it's paywalled now. The abstract, which is not paywalled, says,

[EDIT] My current guess is this. I think Ernst Mach's 1919 The Science Of Mechanics ( http://archive.org/details/scienceofmechani005860mbp ) gradually began to influence presentations of the first law. Influential textbooks such as Millikan's only slightly postdated Mach's book, and were aimed at an audience that would have been unable to absorb Mach's arguments. Later, texts such as Kleppner, which were aimed at a more elite audience, began to incorporate Mach's criticism and reformulation of Newton. Over time, texts such as Halliday, which were aimed at less elite audiences, began to mimic treatments such as Kleppner's.

There is a paper on this historical/educational topic: Galili and Tseitlin, "Newton's First Law: Text, Translations, Interpretations and Physics Education," Science & Education Volume 12, Number 1, 45-73, DOI: 10.1023/A:1022632600805. I had access to it at one time, and it seemed very relevant. Unfortunately it's paywalled now. The abstract, which is not paywalled, says,

[EDIT] My current guess is this. I think Ernst Mach's 1919 The Science Of Mechanics gradually began to influence presentations of the first law. Influential textbooks such as Millikan's only slightly postdated Mach's book, and were aimed at an audience that would have been unable to absorb Mach's arguments. Later, texts such as Kleppner, which were aimed at a more elite audience, began to incorporate Mach's criticism and reformulation of Newton. Over time, texts such as Halliday, which were aimed at less elite audiences, began to mimic treatments such as Kleppner's.

[EDIT] My current guess is this. I think Ernst Mach's 1919 The Science Of Mechanics ( http://archive.org/details/scienceofmechani005860mbp ) gradually began to influence presentations of the first law. Influential textbooks such as Millikan's only slightly postdated Mach's book, and were aimed at an audience that would have been unable to absorb Mach's arguments. Later, texts such as Kleppner, which were aimed at a more elite audience, began to incorporate Mach's criticism and reformulation of Newton. Over time, texts such as Halliday, which were aimed at less elite audiences, began to mimic treatments such as Kleppner's.