See “Why Electric Shavers Are Permitted” at: http://www.koshershaver.info/Kuntris_Magazine_Teves_%205776.pdf
See also Meged Givos Olam (vol. 1, p. 96) where Rav Shurkin writes that he heard that the reason why Rav Moshe did not want to write this teshuvah permitting shaving machines in Igros Moshe is because while
(according to the Igros Moshe) it is technically permitted to shave, the tzurah of a Yid is with a beard.This attestation why Rav Moshe Feinstein zt’l did not publish his heter regarding shaving machines is also recorded in the popular publication Daf Yomi Digest, a daily resource for thousands of Daf Yomi learners
worldwide, compiled by the Ruben Shas Kollel and published by Chicago Center for Torah & Chesed, under the leadership of HaRav Yehoshua Eichenstein shlita and HaRav Pinchas Eichenstein shlita, Rosh Kollel. In their issue on Nazir daf 40, the following is documented as clarification of Rav Moshe Feinstein zt’l’s position:
“It is well known that Rav Moshe Feinstein, zt”l, did permit the use of certain electric shavers. Someone once approached him and asked why he didn’t write a teshuvah outlining the parameters of which shavers are permitted and which are not. ‘After all, your teshuvos cover every subject under the sun!’ Rav Moshe explained, ‘Although I permit this practice halachically, I don’t want to write a teshuvah formally
permitting this since the proper way is for a Jew to have a beard. Although this is not halachically prohibited, a Jew ought to grow a beard!’”
In the most recently published volume of responsa Shevet HaLevi (vol. 11, Y.D. section 198), Rav Shmuel Halevi Wosner zt’l (referred to by many as the Posek Hador) wrote: “With regard to shaving machines…it was agreed by all the Geonim…that there is no difference between [using] them and [using] a razor… The Gaon R. Moshe Feinstein sought to make a distinction between today’s [shaving machines] and a razor
and advanced a theory [in justification]…. That theory is not correct and has not been accepted ( אינה נכונה ולא נתקבלה aynah nechonah v’lo niskablah).”
In addition, in the 5778 issue of Agudas Yisroel of America’s Am HaTorah journal (5:9), Rav Pesach Eliyahu Falk (Rov in Gateshead and author of responsa Machzeh Eliyahu and many other halachic works)
testified that he personally heard from Rav Shlomo Zalman Auerbach zt’l how he rejected the reported reasoning of Rav Moshe Feinstein zt’l to be lenient regarding electric shavers.