Since you haven't cracked open a book on the subject, your above claim is nil. It is very simple: light clocks are not any different from atomic clocks. All clocks are affected the same exact way by the gravitational fields, hence light clocks follow the same exact physics rules as atomic clocks. przyk posted some pictures earlier, you should try finding his post, take a break from trolling and try learning some physics. His pictures tell you that , if the distance between mirrors is $$D$$ , then the amount of curvature is $$\theta=arctan \frac{gD}{2c^2}$$. This is NOT zero, as you claim. Moreover, as time progresses, the curvature of the spiral increases, so, for each bounce off the mirror, the photon path deviates from a straight line more. .
Then that should mean the photon would soon 'pop out of the bottom" of the mirror system in a light clock with vertical mirrors? Has this been observed? Unless it has, then your assumptions/equations do not represent the reality.
Like I said, I go by the mainstream claim that over very short distances the "curvature" is essentially nil, and so cannot account for the observed significant slowing of the rate. Brucep and other mainstreamers have claimed so many times.
Which is why the differing gravitational potential "energy density" in that local frame space is the logical effective factor in the clock tick rate differences between differing altitude GR frames.
Which is why I again refer you to another mainstreamer (Markus Hanke) comment:
Markus Hanke said:"curvature is energy!
I agree with Markus on that. And since we all agree that physics is the same for every frame, then the common denominator for variation ("curvature" etc) of the observed effects must be the local frame energy density affecting all clock processes therein. Yes?