You asked two questions:
Two questions -- one, is there any direct corroboration for Rosenfeld's statement that one should not say the bracha in shacharit?
The Yekkish Minhag is to do as Rabbi Abraham Rosenfeld writes, and is how our Kinoth books instruct us to behave, dating back over 100 years ago. (As can be seen in this Kinoth book from 1945)
Our Avodath Yisroel Sidur, edited by Rabbi Yizhak ben Arie Yosef Dov (Seligman Baer) in 1868 also records this Minhag, bringing no source.
Two, would that mean Rosenfeld would delete the bracha on all days when we don't wear tefillin at all?
No. He can't mean that since saying this Bracha belongs to covering one's head, as we learn in Brachot 60b, כי פריס סודרא על רישיה לימא ברוך עוטר ישראל בתפארה - when you cover your head you say this Bracha.
This is codified by the Rambam (ספר אהבה-הלכות תפילה וברכת כהנים - in 7:8) - כְּשֶׁמַּנִּיחַ סְדִינוֹ עַל רֹאשׁוֹ מְבָרֵךְ בָּרוּךְ אַתָּה יְיָ' אֱ-לֹהֵינוּ מֶלֶךְ הָעוֹלָם עוֹטֵר יִשְׂרָאֵל בְּתִפְאָרָה.
And then ratified by the Shulchan aruch - Orach Chaim 46:10 - כְּשֶׁמֵּשִׂים כּוֹבַע אוֹ מִצְנֶפֶת בְּרֹאשׁוֹ, יְבָרֵךְ עוֹטֵר יִשְׂרָאֵל בְּתִפְאָרָה.
This, despite the fact that in 25:3 he mentions that - as Rabbi Abraham Rosenfeld taught you - הָרֹא''שׁ הָיָה מְסַדֵּר הַבְּרָכוֹת עַד עוֹטֵר יִשְׂרָאֵל בְּתִפְאָרָה, וְאָז הָיָה מֵנִיחַ תְּפִלִּין וּמְבָרֵךְ עוֹטֵר יִשְׂרָאֵל בְּתִפְאָרָה - that the Rosh would put on Tefillin right before saying this Bracha.
But obviously only on weekdays. Otherwise the Shulchan Aruch would have mentioned your suggestion.
Conclusion: This Bracha also refers to Tefillin. To highlight the fact that we don't put on Tefillin on Tisha B'Av because of the mourning (as we already discussed elsewhere) some have the custom to also omit the related Bracha.
(BTW: The Kitzur Shulchan Aruch in 59:8 says - יֵשׁ אוֹמְרִים דְּהַקּוֹנֶה כּוֹבַע, כְּשֶׁמְּשִׂימוֹ בְּרֹאשׁוֹ יְבָרֵךְ עוֹטֵר יִשְֹרָאֵל בְּתִפְאָרָה - that some have to custom to say this Bracha when buying a new hat.)