You are absolutely correct in your thinking. We should be saying some type of food bracha on tefillin, because after all, one of the verses relating to tefillin says:
וְהָיָה֩ לְךָ֨ לְא֜וֹת עַל־יָדְךָ֗ וּלְזִכָּרוֹן֙ בֵּ֣ין עֵינֶ֔יךָ
לְמַ֗עַן תִּהְיֶ֛ה תּוֹרַ֥ת יְהוָ֖ה בְּפִ֑יךָ כִּ֚י בְּיָ֣ד חֲזָקָ֔ה
הוֹצִֽאֲךָ֥ יְהֹוָ֖ה מִמִּצְרָֽיִם׃
And it shall be for a sign unto thee upon thy hand, and for a memorial
between thine eyes, that the law of the LORD may be in thy mouth;
for with a strong hand hath the LORD brought thee out of Egypt.
Since the tefillin contain words of the Torah, a great way to put the Torah in your mouth would be to eat your tefillin. And, of course, since the tefillin are called "pear", and we're not supposed to eat anything without making a bracha first, we should be saying Borei Pri Ha'etz.
The reason we don't eat our tefillin is because if we did, we would be erasing G-d's name. It's not the chewing of the tefillin that would be the main problem. The acid in the stomach would completely destroy G-d's name, and we're not allowed to do that. Therefore, we have to wear these pears on our arms and heads and deal with these fruit on our bodies.