1) The Mordecai explains this in Halachos Ketanos, which is printed at the end of Gemara Maseches Manachos (this is where the Mordecai and other Rishonim write the Halachos of Tefilin). It is on page ?? column 4, at the end, in the older editions of the Gemara (or page 26 column 2 at the end) and is cited by the Beis Yosef on the Tur Orach Chaim #43 DH u'BeNichnas.

The Mordecai writes in the name of BeHaG that we learn from what Rabbi Yochanan did, that one should not give one's tefilin to one's friend before entering the bathroom.

2) The Talmidei Rabeinu Yonah (printed on the side of the Rif at the back of the Gemara 14b in the Rif pages DH Ho'il) writes that some explain the word "Ninteran", that we have in our text of the Gemara at the very top of 23b, to mean "I will guard the tefilin myself". Beis Yosef writes that it seems that the Mordecai agrees with this explanation. It appears that Rabbi Yochanan held that it is a Mitzvah to watch over the tefilin oneself and not to give the tefilin to one's friend. Beis Yosef writes that alternatively one can say that the Mordecai learnt like Rashi; that the tefilin will protect him from the demons. Therefore it is better not to give the tefilin to a friend, but rather to take it in oneself, so that it will provide protection.

3) It seems to me that it is not difficult why the Gemara did not utilize this reasoning previously, because it was only after the tragedy, when the talmid fell off the roof, that the Takana was made that one should hold the tefilin in one's hands and enter the bathroom. This meant that Chazal made a Halacha that in order to protect the tefilin one may take them into the bathroom. Rabbi Yochanan took this slightly further and said that to protect oneself from demons one may also take the tefilin in.

Dovid Bloom