In my own supplement on Tauric races*, I went with what I felt was a more complete and explicit route of having them be large creatures, except with the limitation of using medium weapons (and thus medium weapon damages), rather than this UA's route of "no, you're medium, except you can carry more". Both are wordy and a bit of a kludge, but to me keeping them large feels both more right and also preserves more of the downsides, and still prevents the main thing: giving Centaurs (And other taurs) access to higher-damage weapons.
(Which is important; I've played Centaurs often over the years, and being able to dual-wield a two-handed sword plus a bastard sword because you were considered large was... well, fun, to be sure, but both kind of ridiculous from an aesthetic sense and from a game balance sense.
![Stick out tongue :p :p](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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Regarding natural weapons (and I'd do the same for the Minotaur), as "rider"-ish as they seem, I concur with leaving them at middle-of-the-road damage, though I explicitly called them out to be finesseable, and included a feat to bump the damage up for those who'd like to make them their prime weapon. Personally, if a player wanted to use their natural weapons as their main shtick, presented it to me and I can see that it's in line with weapon users, I'd likely allow it, and even plan a scenario or three where the benefits of it being a natural weapon (that can't be removed/lost/etc, for example) shines so that the character can shine in that moment.
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On the one hand, I can understand that they didn't want to do a long write-up for a UA post, but I am still surprised they didn't at least mention this in a sidebar. Considerations for playing a taur character took up a couple of pages when I wrote my supplement, it's an important aspect that can add both fun but also frustration if it's not accounted for and discussed in a long-term campaign.
On four hooves (or paws, or...),
Kannik
*
http://www.dmsguild.com/product/207056/Tauric-Races-Centaurs-Wemics-Formians-and-more