Yeah, you can dual spec both specs. But in any case, to humor you, both Holy and Shadow are very popular specs for the class. Shadow being the obvious dps spec for the class in addition to being a "mana battery" for healers (which people LOVE to have btw). The Holy spec is really popular for its strong throughput, Improved Divine Spirit (for more mana regen and bonus spell damage!), and is valued for a variety of its abilities in various types of content. Such examples include Fear Ward (which is loved by tanks in dungeons and some raid encounters), Shackle Undead (amazing in Kara, btw!), Mind Control (very niche in pve, like using one of the mobs in the Botanic to give your group a +250 sp buff for 30min!). But more importantly, a Holy Priest, while it may lack in number of utilities compared to the other healer classes, a Priest is always wanted for its raw throughput and wonderful mana efficiency abilities and stat builds. Every raid will want at least one Priest for each of the two specs, even if they might not have room for them in Kara (because 10 man raid size rip).
If you're wondering what global is spamming for, though, it's tanks and Holy Priests. Usually. Mostly tanks though.
Not completely serious on that, but I did see a lot of spam for Holy Priests in global here the other day.