Question

Why is chemical energy not accepted as a viable method for energy generation in the sun?

Answer 1

I know of two reasons.  I'm sure there are more.

#1).  No chemical process can account for the distribution of energy
that we see coming from the sun.  I mean the portions of the total
that are radio waves, heat waves, light waves, x-rays, and gamma rays.

#2).  A pile of the most energetic known chemicals, with the mass
and volume of the sun, in the process of reactions and emitting
energy, would have been burned out, all over and done with, long ago.   

I read somewhere many years ago that a pile of coal the size of
the sun could burn for 160 years.  Even if it were ten million times
as long as that, it would still be way short of the 4.6 billion years
that the Earth has existed.