Why Fructose?

Today I learned that only the fructose phosphotransferase system (PTS) is present in the Rd strain of Haemophilus influenzae. This means that H. influenzae cells rely on fructose as their primary source of sugar. This is odd considering glucose is much more abundant in respiratory mucus where we would expect to find H. influenzae (meaning it would make more sense if the cells relied on glucose rather than fructose). When the cell's preferred sugar is not available, the cell turns on genes that allow use of other sugars (and also, the cell turns on it's competence genes and becomes ready to uptake DNA).

I was just thinking about this and I hypothesized that perhaps the cell relies on fructose because it wants to turn on it's competence genes often - thus relying on a scarce sugar would keep the cells competence machinery in production more often. I also thought that perhaps it's actually more effective to use DNA as a source of energy than glucose, so I took to the internet and I tried counting expected ATP output for glucose vs. nucleotides:

Glucose
+2 net ATP from glycolysis
+2 ATP from citric acid cycle
+32 from electron transport chain (let's say)
36 net ATP production from glucose breakdown

To transport glucose using a PTS system, it requires an equivalent of 2 ATP, however one of these reduces the amount of ATP needed in glycolysis by 1 so it costs 1 ATP to transport glucose into the cell.

Nucleotides
I'm going to assume the cost of breaking dsDNA down into deoxyribose and nitrogenous bases is 0 which may be entirely wrong.

Deoxyribose
-1 ATP to split into glyceraldehyde-3 phosphate and acetylaldehyde
+18 ATP since glyceraldehyde-3 phosphate undergoes half of glucose catabolism
+1 ATP to balance the fact that an early energy costing step of glycolysis was skipped
+14 ATP produced from acetyl-coA and NADH produced from acetylaldehyde
32 net ATP production from deoxyribose breakdown

Nitrogenous base
De novo synthesis of a base is 4 ATP so I will say that the base is worth +4 ATP since rapidly dividing cells are always in need of bases.

That makes 36 ATP molecules per nucleotide which means the two break even in terms of energy yield. The real question is how much energy does it take to uptake DNA per base? I don't know if the answer's known. If it's less than 1 (since entire strand are taken up), than it's possible that using DNA would in fact a more effective way to produce energy than sugar.

I don't think that the cells would rely on DNA over sugar for energy, but it was fun to do the accounting. I know there's a lot of DNA in mucus and that any sugar supply would be competed for by the host cells, so there is some reasoning behind this idea, but again, I'm not really convinced.

Also, to get these ATP values, I had to look at biochemical pathways and just count the reactions that required ATP. There may be errors (ie. that fact that I was using mostly human pathways since more information is available) so if you see them, let me know with a comment.