Rashi explains that כובד ראש means הכנעה - submissiveness. "The pious men of old used to wait an
hour", explains Rashi "in the place that they came to daven" - במקום שבאו להתפלל
In maseches rosh hashana [26b] there is a similar discussion of how one should daven - in a submissive lowered fashion or in an elevated state with the attendant halachic ramification of whether the shofar should be bent or straight. That sugya is ALSO strangely not mentioned here.
Our mishna says that the pious men of old would "wait" an hour before davening. It would have been more appropriate to say that they would "have kavana" for an hour or "prepare their hearts" for an hour. The "waiting" seemingly is not part of the actual davening but something else.
Apparently, that is why Rashi explained במקום שבאו להתפלל - In the PLACE that they came to daven. Why do they have to wait in the "place" they came to daven? Let them do so at home or elsewhere?!
The answer is that our mishna is not telling us a law in the realm of the actual davening but in the PLACE where we daven.
That is also why the mishna uses the language אין עומדין להתפלל "We only stand up to daven" when it could have said אין מתפללין which relates directly to the davening itself. But with this new insight that the mishna is discussing a law in the PLACE of tefilla we understand the emphasis on the STANDING for davening.
It is now automatically understood that the sugyos of yevamos and rosh hashana that I mentioned have nothing to do with our sugya as they are discussing the actual tefilla and thus are not quoted here.
This explanation is especially compelling according to Rav Yosi ben Rebbe Chanina in the gemara who derives the law of davening בכובד ראש from the pasuk ואני ברוב חסדך אבוא ביתך אשתחוה אל היכל קדשך ביראתך - This pasuk indicates a law of "biah" - coming to the place.
This "geder" of a special place is indicated by the gemara [26b] that states אין עמידה אלא לשון תפילה.
I believe that these words are נפלאים בהבנת דברי המשנה.
[Based on the as of yet unpublished sefer - and looking for a sponsor - Marbeh Tefilla Simman Aleph by my Rebbe, HaRav Yaakov Dovid Homnick Shlita.]