Short answer: there is no reason. It is just a random value.
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The measured value of the fine structure constant is
α = 1 / 137.035 999.
https://en.wikipedia.org/wiki/Fine-structure_constant
The fine structure constant is, among other things, the ratio
electron classical radius
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radius of the electron charge spin loop
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radius of the electron charge spin loop
The charge spin loop means the imagined circle which the electron charge makes at the speed of light, and which produces the electron magnetic moment. The radius is
r_m = λ_e / (2 π),
where λ_e is the electron Compton wavelength.
The electron mass spin loop radius is
r_s = 1/2 r_m.
The mass spin loop is the imagined circle which the electron mass makes at the speed of light, and which produces the spin angular momentum.
The classical radius is determined by the energy density of the electric field and the mass of the electron.
In a sense, the fine structure constant is the ratio
energy density of the electron electric field
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Planck constant.
Does this ratio have a random value or is it determined through some physical mechanism? The numerical value of the ratio looks random.
The role of the fine structure constant in the photograph model of quantum field theory
Let us analyze the fine structure constant from the point of view of our photograph model.
The Planck constant determines the resolution of the photograph of classical processes. It determines how "sharply" we can see the deep down classical processes. Let us call our impaired vision the Planck microscope.
The electron electric field and its energy density are classical physical things. They are things which we look at through the Planck microscope.
Conceptually, the Planck constant is at a different level from the electric field. The Planck constant is much more fundamental. The electric field is just a random object which we look at through the Planck microscope.
It would be surprising if the Planck constant would be related to a random field in nature - the electric field. Thus, there probably is no deeper reason for the value of α.
Which things in the electron are classical and which are quantum (i.e., wavelike)?
Electromagnetism is a classical thing. The electric field of the electron is classical.
The existence of the spin is a quantum thing. It is required by the wave description of the electron, to conserve the number of particles.
The angular momentum in the spin is a classical thing. But we look at the angular momentum through the Planck microscope, which makes it behave in a quantum way.
The magnetic moment of the electron is a classical thing. The fact that the gyromagnetic factor is 2, is a quantum thing which arises from our impaired vision through the Planck microscope. We cannot see the mass spin loop because it has too small a radius.
The mass of the electron might be a quantum thing because the classical mass-energy of its static electric field is infinite. Another possibility is that the classical mass of the electron (if any) is in the point particle, and the "true" mass of its static field is zero. The field can store momentum, but it might be a result from retardation, and "tension" of electric field lines.
We will look at the mass problem when we analyze diverging Feynman diagrams.
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