In the three years and ten months since the last post in this thread, we have received two incredible special series.
First, Pokémon Origins, which first aired a scant few months after the last post, in October of 2013. Now that was a glorious mini-series. It was essentially Red and Blue, condensed into four OVAs, with solid voice acting (I'm quite fond of both the dub AND the sub), a fun story, and some very intense action. One of the most noteworthy things about it was just how dark it was, compared to the regular anime. Many people compared it to PokéSpe, aka Pokémon Adventures, which is the most well known of the manga adaptations. And, to top if off, this was how Mega Charizard X was officially revealed, which is ridiculous in the best way possible.
Moving on, to September 2016, about seven months ago. This is when Pokémon Generations came out, which, as an avid TCG player, briefly confused me, due to the TCG subset of the same name. Generations was an absolute treat. It's what's known as an ONA, or Original Net Animation, series, which gave the powers that be more flexibility. Short episodes, ranging from around three to five minutes, that encompassed interesting parts of the story of the games that lacked attention in the game. The focus was on side characters, and honestly, it was incredible.
So, to answer the question posed in the title, I absolutely think that there should be more specials. As for what kind? I want a Pokémon Origins for each generation. I'd also love if Generations would continue with Sun and Moon shorts, as the games have been out for awhile now.