In this blogpost the contention is made, based on many rabbinic sources, that unfortunately the observance of the miswa of tefillin was weakly observed during various historical periods. The author of the post has his own theory for what caused a revival in observance (the influence of Lurianic kabbalah). Earlier however, in Michael Levi Rodkinson's History of the Talmud (p. 31), it is suggested that a shift in widespread observance was a reaction to Karaite denial that tefillin are intended by the Torah (Ex. 13:9; 13:6; Deut. 6:8; 11:18):
The effects of Karaism are also traceable in some religious practices, which had not been usual among the people of ancient times. Thus Phylacteries, which it had not been customary to use, in spite of the literal interpretation of the Talmud of the passage " and thou shalt bind them for a sign upon thy hand, and they shall be as frontlets between thine eyes," (Deut. vi. 8) ; perhaps for the reason that Hillel had said: "Leave Israel alone; if they are not prophets, they are children of prophets," (Pesachim); for after all, the arguments of the Talmud in favor of the literalness of that passage, the people felt that it was only a figurative expression; and the Talmud itself prohibited the use of phylacteries to the people, permitting it only to con-firmed scholars. But when the Karaites interpreted the passage figuratively, the Gaonim permitted the use of Tephilin to the people also, to show their difference from the Karaites.
The notion that there were those that mistakenly believed that tefillin are solely the province of scholars, can be demonstrated by the responsum of R. Sherira Gaon (cited in the abovementioned blogpost). The idea that certain practices were prescribed or strengthened as response to Karaism I don't find altogether unique either (such as some suggest as the basis for the consumption of chulent/hamin, or the recitation of bameh madliqin on Friday night, etc.). However that the Geonim sought to bolster the practice of wearing tefillin specifically as a hedge against Karaism seems to me to be a unique claim.
Does anyone know where Rodkinson got this idea from? Is there any support for it? Do any other scholars (traditional or academic) discuss it?