But I still don't see why it should make any difference in regard to the detergent?
The top loader powder is more concentrated and produces more suds. That's why the manufacturer does not recommend it for front loader machines, because too many suds in a front loader can stuff-up the works.
Because front and top loader powders come in the same size box and are the same price, and because the top loader powder is more concentrated than the front loader powder, by using the top loader powder in a front loader machine, you can get away with using only half the recommended powder and, therefore, getting double the amount of washes from the same amount of powder.
And Fritz makes a very valid point about water temperature. I recommend using a bona fide cold wash powder, with all the savings that attracts. I have been using cold water wash for years and my wash is always very clean.
Unless you work in coal mine, it is most likely that your clothes do not need the longest, most powerful wash your washing machine provides. I always use the briefest wash cycle (I'm an office worker - my clothes never really get "dirty" as such) with all the associated savings that attracts.