When tempering chocolates, we want that the chocolate will only contain beta crystals, for this, we melt the chocolate to a point where all crystals break, then cool it down to below the melting point of beta crystals, and then warm it back up to working temperature, which is just below the melting point of beta crystals. In many sources the lowers temperature to get to is 27°C, see for example this video by Callebaut Chocolate.
According to the Tempering section in the chocolate Wikipedia page, there are 6 types of crystals:
Crystal | Melting temp. | Notes
--------+-----------------+-------------------------------------
I | 17 °C (63 °F) | Soft, crumbly, melts too easily
II | 21 °C (70 °F) | Soft, crumbly, melts too easily
III | 26 °C (79 °F) | Firm, poor snap, melts too easily
IV | 28 °C (82 °F) | Firm, good snap, melts too easily
V | 34 °C (93 °F) | Glossy, firm, best snap, melts near body temperature (37 °C)
VI | 36 °C (97 °F) | Hard, takes weeks to form
Where it's obvious that we want only crystals of type V, but lowering the temperature to 27 °C, just below the melting point of the type IV crystals, allows them to be formed, before they are broken in the reheating.
Why do we allow chocolate to go below 28°C and allow type IV crystals to form, and not stop the process at 29°C?
Best Answer
This YouTube video from America's Test Kitchen doesn't exactly address your question, but I think it hits it on the periphery towards the end.
Summary: Dan (the chef) goes over the traditional way of tempering chocolate (much like the method you link to / describe). Then, he goes over their shortcut version. In the shortcut, most of the chocolate is heated until it just melts in the microwave, then the remaining chocolate (having been very finely chopped) is added in (and microwaved in 5 second bursts, if it doesn't melt with the residual heat). The result is close to, but not exactly the same as the traditional method.
My take-away and guess as to why: In the traditional method, a mix of type IV and V crystals are formed, but, I suspect that there are also some quantity of type III as well (in small pockets that are not the same temperature as the rest of the mixture). I suspect that the creation of the different types helps keep crystal sizes small - which is one of the desired conditions of tempering. By allowing the mix of small crystals to form, then melting the undesired ones, you may be allowing more smaller crystals a chance to form, instead of larger one. If this is true, it might explain why the second method produces a slightly inferior temper: the seed crystals might be too large (from the just recently melted chocolate), and their initial growth is uninhibited by other crystal types.
I've just checked with my BakeWise book (tempering chocolate p 104-107) by Shirley O. Corriher (Amazon link). On pg 106, she mentions that cooling dark chocolate to 82F/27.8C ...
She also mentions stirring constantly several times over. This is usually an indication that one is trying to A.) keep temperatures uniform throughout a mixture and/or B.) promote small crystal growth. (It's why ice cream makers constantly churn, instead of just chucking the mixture into a freezer.)
So, I'm going to stick with: formation of lots of small type V's, even with some type IV's, is more desirable than the formation of fewer type V's, but with no type IV's.