The trouble is that most humans are very impatient. Furthermore, almost every yeast loves to eat all the simple sugars of which cider is comprised almost 100%. With just about any yeast you can imagine, cider needs a long time to finish fermenting, longer than many would think. Sure, you can hit SG of 1.000 with ease in just 2-3 weeks. However it's often those last few points down to the minimum of 0.992 (that would be my "confidence level" for SG) that take a whole 'nother month. Many beer brewers will follow the old rule of thumb of "check gravity over the course of 2 or 3 days, if gravity doesn't change then it's safe to bottle". Not true with cider. Give it another 2-3 WEEKS between gravity readings if you want to really be safe and sure that you've hit final gravity.
Once you are positive that you've hit final gravity, then you can certainly prime and bottle without any trouble.
KEY POINT: Most people also seem to want sweetness in addition to carbonation. Getting both is the struggle, because the yeast will want to eat all the backsweetening and thus explode your bottles. It's not so easy to get both sweetness and carbonation in your bottles.
My methods (discussed in other threads) of racking often, knocking out yeast with gelatin, chilling, and being patient for many months have worked out well for me. I can often get carbonation in my bottles, AND have some sweetness left as well. Unfortunate for many people, this does require more time than they care to wait. Like, 6 to 9 months, ballpark. The excited new cider maker will probably drink all the cider before it gets carbonated, then complain that it's all flat, or conversely, use a ton of backsweetening and end up with gushers and bombs. It's difficult to expect speed and sweetness and carbonation all at one time.
Of course, if you keg it, then there's no worries. These concerns are all specific to bottling.
That's sort of the long-winded explanation. In my experience, laziness I mean patience has really been the key to the whole thing, if you want a well flavored, well carbonated, and slightly sweet homemade cider.