You are right. The easiest way is to memorize that after "Почему бы" you have dative + "не" + infinitive. Frankly speaking, I have no ideа what rule works here, but it happens this way. Почему бы тебе не сделать... Почему бы ему не пойти.... Почему бы мне не купить... Почему бы твоим друзьям не написать...

Wei, хорошо бы мне купить... зачем мне покупать.. зачем бы мне покупать... мне надо купить... In Russian dative and infinitive often express modality. In Russian expressions that mean "I need", "I should", "it is better for me to..." we often use dative and inf.: мне стоит купить - I should buy - literally: "for-me it-makes-sense to-buy" мне надо купить - I need to buy - literally: "for-me it-is-necessary to-buy" мне лучше купить - literally: "for-me it-is-better to-buy" These examples look more or less logical in English! We also say: мне хочется купить - I want to buy - literally "to-me it-wants-itslelf to buy". ("я хочу" means conscious wish, while "мне хочется" is more like I feel an urge) мне предстоит купить - literally: "for-me before-stands to-buy". I don't know how to say this in Enlgish. It means it is your future to buy it:) In all this cases dative is caused by "better (to whom?)", "it is necessary (for whom?)" and so on. But we generalized this. We also say: casually: Мне купить диван? (should I buy...?) Мне завтра покупать диван. (omitted "надо/предстоит") Less casually: Трампу не победить на выборах! (It is above Trump's powers to win the elections or Trump is not destined to win the elections) In other words: "We" can not be subject of infinitive. You say "I want", not "I to want". "We" is connected to infinitive by some word expressing desire, necessity, destiny, modality. Such words cause "we" to take dative. In absence of such a word Dat and Inf are also understood as... something like this. Some modality. But in Russian we don't have a modal question word - so we just add "why". The closest thing is: Не лучше ли нам купить... ? Is not it better for us to buy...? Не стоит ли нам купить... ? We also can say it without dative: "почему бы не купить диван"? Why not buy a...?

You have a good level of German. I think my knowledge of Russian helps me a lot in learning German, so maybe your knowledge of German can help you with Russian =) Ich kaufe (wem? Dat) jemandem (was? Akk) etwas Я покупаю нам (Dat) новый диван (Akk) Mascha schreibt (wem? Dat) ihm. Маша пишет ему (Dat) Like in German verbs have cases and prepositions that sometimes must be learned, but more often can be "felt" or understood. Good luck!