Actually I was just enjoying this light a few minutes ago. Its an awesome piece of engineering, as is my Fenix TK41 and TK50. I have this problem that each are my favorite light when I pick them up. All three are that good.
To answer your question, no, the LD22 with XP-G2 has the same problem with low mode when using fresh alkalines. Same with my TK41 U2 model, and my TK50. As I understand it, the issue is not with the specific emitter any particular light is using, but with the boost circuit Fenix uses and how it handles the relatively high voltages of brand new alkaline batteries.
And yes I know that you know it works fine with Eneloops and you're asking about alkalines but.... jeez, get yourself four eneloops and a decent charger and all your (LD22 related) problems will be solved!
Seriously, they really are awesome technology and worth the investment. Four Eneloops beat alkalines in almost any plausible scenario involving this light. And in any scenario where they don't, you're probably not missing Low mode in the preliminary stages of the alkaline batteries' life.