Am I supposed to hover over every debuff to see if (1) I can even remove it and if (2) it's even worth the time and mana it would take to remove it? Or are healers expected to memorize what each tiny little icon means along with 1 and 2 as mentioned before?
Knowing about debuffs is part and parcel of being a healer, even if you can't remove them. For example, Mortal Strike debuffs have a fairly drastic effect on your ability to keep the tank alive. Many raid encounters have debuffs that are absolutely critical to know, regardless of whether you can or cannot remove them.
It's really that part and parcel of healing is understanding the fight mechanics rather than just making green bars go up whenever they go down.
In this specific case, the disease ticks for 4k damage. If not removed, it will keep jumping to another person when it runs out (and will do that indefinitely as long as people are close). It's also much more efficient to just cure the disease than to heal the 28k damage it does over time even if it weren't jumping.
Addons can help you quickly classify debuffs by type, but, as I said, it's often just as important to know the ones you can't remove. Sometimes you also don't want to remove them even though you could. For example, in Halls of Reflection, you generally want to dispel both magic debuffs generated by the first boss (one stuns the victim after a few seconds if not removed, the other reduces tank dodge chance by 20%), while the magic debuff produced by the second boss is a judgement call (it's a DoT that will do damage to the entire party if removed; whether that's beneficial depends on whether somebody stood in the damage-amplifying curse -- and that curse is another debuff that everyone needs to know about whether they can remove curses or not).