Actually, there are a few reasons for using non-rechargeable batteries (but none that I can think of why you shouldn't use them for your gameboy...)
- much higher capacity of Alkaline batteries than rechargeables.
- much longer shelf life of Alkalines (10+ years); rechargeables tend to self-discharge, even when not used. NiMH are especially bad, they discharge at 1-2%/day.
- higher voltage of non-rechargeables (about 1.5-1.6V when fresh)
- lower price of non-rechargeables.
and probably a few more reasons I can't think of.
I like alkalines for several applications, like torches, that are used only very infrequently but absolutely certainly have to work when I need them. I've found NiCds always to be empty when I needed them. I can put alkalines in a torch and not worry about it for a few years. No leaks (AFAIK, alkalines don't leak; and, AFAIK, no battery that's full leaks; only discharged ones).
IMHO, there are no reasons for using non-alkaline batteries. It's either alkaline or rechargeable (pref. NiCd when self-discharge is an issue; NiMH when higher capacity is needed) for me.
BTW, us folks don't have an interest in anything. It's the manufacturers and special-interest groups that you've got to be careful of. In here you'll find lots of information, usually non-biased. Also, you will find a lot of conflicting information. Thinking is required, as always.