Dodging works ... to an extent. You need to be
spectacularly fast to dodge a polearm swing from a skilled wielder because you're trying to move your center of mass while they need to just roll their shoulders to be hitting an entirely different spot. Zelda-style dodge rolls only work because of iframes and the limitations of early 3d graphics. Your nine year olds are good at dodging you using only your arms - and even then they still lose a lot I expect.
It's unfortunately not bizarre to see someone more concerned with the texture of someone's skin than the serious physical day to day issues that they would have to deal with to operate in a reasonably normal society.
And Tolkien's hobbits worked because they were basically non-combatants and needed protecting. The Lord of the Rings was an escort mission that went really wrong. D&D is very combat centric.
As for popularity of gnomes vs halflings
D&D Beyond and 538 released some data - halflings are more popular than gnomes but not by much (although half orcs are in the middle). Almost all the short rogues are halflings and the short wizards are gnomes - halflings also get monks and oddly enough bards.