There is no halakhic reason for Ashkenazim to be makpid on glatt.
You’re wrong under almost (if not literal) every definition of “glatt”.
1) If glatt is used in the vernacular, it refers to a general higher standard. Of course there’s a reason to be makpid on a stricter standard of who is a yarei shomayim for shecitah and bedikah (as an example).
2) If glatt is used as in “OU glatt”, which is acceptable for Ashkenazim but not Sefardim, then “not glatt” would refer to a looser standard, within the Rema’s shittah, of how easily a sirchah is removed yet still considered glatt.
3) Even if referring to Bais Yosef glatt (which in this case it isn’t), saying “there’s no reason” ignores the fact that the Rem’a himself refers to it as a “kula gedolah”, and that many yorei shomayim, even Ashkenazim, are makpid on the Mechaber’s glatt.