Why couldn't he not think of something like a triangular or any distorted shaped atom (and why only a spherical one)?
Can't the positive charge be in some other fashion which is not evenly distributed?
Can't it be that positive protons are present in a sea of negatively charged electrons?
The honest reasoning in favor of the so-called "plum pudding" model is available in a number of public-domain sources from that time period. You might enjoy the 1914 article The Structure of the Atom in Nature No. 2308.
It was known at the time that corpuscles of negative charge (now called "electrons") could be extracted from an atom, leaving a positively-charged particle (now called an "ion") of approximately the same mass as the neutral. Both the neutral and its ion, if they had a shape at all, must have been spherical in shape, since they showed no angular dependence in interactions with other particles. No fundamental corpuscle of positive charge could be extracted from a neutral. Therefore, the reasoning goes, the atom must consist of its "electrons" as well as a heavy positively-charged part. What's more, since positive and negative charges attract one another, these charges must pull themselves into a compressed, isotropic volume. The simplest model (for we do so love simplicity) then has the electrons distributed throughout a positively-charged sphere.