The artist is Daniel Chester French. It's interesting that you perceive the statue as villainous. To answer your question directly, though: I've never a critique on that quality.

By way of a little context, French did intend to make Lincoln appear formidable. However, he also used subtlety of expression, pose, and especially details in the hands to convey Lincoln's humanity. (I'm not sure "folksy" is exactly how he was perceived, really. His roots were humble, but he was well spoken and learned.)

Notably, French and Henry Bacon, the memorial's, architect, had originally designed a much smaller, standing statue. They ultimately felt that a bigger, broader statue would fit better with the surrounding architecture. The building itself is based on Greek and Roman principles of balance (the statue is exactly as high as it is wide) and democracy (his chair arms are capped with bundled reeds, a classical symbol of unity).

Lincoln's seated pose is relatively casual and helps to bring the figure down the the viewer's level. The figure is slumped and his head is bowed, evoking the burden he had carried. He is gaunt, with heavy-lidded eyes, mussed hair, and a crooked tie, recalling the exhausting toll the war took on him and the nation. One of Lincoln's hands rests lightly on the chair, representing his openness and compassion. The other hand is semi-clenched, possibly representing determination. But even that isn't a fist. The way the thumb sticks out looks like a habitual gesture: the way some people will rub their thumb against their index finger while deep in thought.

As a follow up question - what were the inspirations or sources of influence for other presidential monuments in the D.C. area, and why did they differ?

I know, for instance, the fresco on the Eye of the Capitol Rotunda was based off of classical and Renaissance depictions of Zeus/Jupiter/God various religious or mythological figures (edited to be more inclusive), would be interesting to know if memorials to Lincoln (or Jefferson, etc) has similar or different influences when first designed, and if they were interrelated in any way.