Why are molecules such as allolactose (for lac repressor) or 2,3-BPG (for haemoglobin) used for allosteric regulation rather than the actual molecules involved in biochemical pathways, such as lactose and 1,3-BPG? The formation of such "extra" regulators requires energy – what is the advantage of such organisation?
It's an interesting question, and there are a lot of potential explanations.
I can at least hypothesize a little bit for the case of 2,3-BPG and 1,3-BPG. I think the key point is that it's not obvious to me why sensing the 1,3-BPG concentration would be useful. This concentration actually has to be maintained in a pretty tight range for glycolysis to function (note that the entire lower portion of glycolysis is very close to thermodynamic equilibrium). The reason that I think 2,3-DPG is a useful regulatory molecule is precisely because its levels can be regulated independently of the function of glycolysis. The activity of the enzymes in the 1,3-BPG -> 2,3-BPG -> 3PG shunt can controlled independently of the control of normal glycolysis and can be regulated by whatever physiological parameter you want 2,3-DPG concentration to represent.
One other thing to note is that typical red blood cell concentrations of 2,3-BPG are actually many orders of magnitude higher than 1,3-BPG. The very low concentrations of 1,3-BPG are a necessary consequence of the thermodynamics of glycolysis as mentnioned above -- if 1,3-BPG concentrations are too high, the GAPDH reaction will become unfavorable. Thus it may be that the typical concentration of 1,3-BPG is too low to be an effective regulator of anything (because it would have to bind very strongly). But I think this is a less important point than asking the question of "what does the concentration of my regulator represent".
There may be biochemical reasons at work in other cases -- for instance, some molecules may just bind better to the protein that you want to regulate, and that's why they're chosen by evolution. I think this is a case when it will be hard to come up with a blanket explanation -- it's better to look at each case, consider what signal biology is trying to measure, and look at the relevant constraints.
I don't know the answer for 1,6-FBP and 2,6-FBP, and note that in other species, 1,6-FBP does appear to be the major regulatory molecule. You could argue that by having 2,6-FBP be the regulator, there are more enzymes whose activity you can control and thus somehow you have more fine-tuned regulation