"However, I can often hear people [...] say, for example:
I wanted to remember it for all my life.
I've been waiting for this moment for all my life."
So, do people break the grammar rule saying something like "For all my life, you'll be the one"?
Let's cut to the chase. Yes, in each case, these examples, represent people breaking rules of grammar. However, I would qualify this by saying that in spoken English, either form is acceptable.
This subject has been canvassed in this place at least once previously Is there a grammatical rule impeding the presence of 'for' in “I have lived here 'for' all my life”?. On that occasion there were views for and against. Some relying on standard academic publications to reinforce their views. The most popular answer was "I think you just have to accept that when all comes before words that express any length of time, it cannot be preceded by for".
J.R (reputation >94K in this community) also entered the fray and his comments are most relevant to this question. He said "Unless the for is not starting a prepositional phrase (as in, "That is what I've been hoping for all my life," or, "This is what I've been waiting for all summer")."
The topic has also been canvased, to a lesser extent, on "English language and usage" Difference between “my whole life” and “all my life”?. Interestingly, the responses there were somewhat less didactic
The questioner asks specifically about the sentence "For all my life, you'll be the one". I don't think there is any doubt that this breaks the formal rule of not using "for" in a prepositional phrase. But how easy is it to imagine two lovers saying these words to each other? At that time and place, do the laws of grammar apply? Which is why I believe that in spoken English the rules are not so hard and fast as they might be for written English.
In any event, though I am a stickler for grammar (or at least the bits that I know of), I think grammar rules are made to be broken. How else does language relate and respond to daily life, new experiences and events, if not through constant change? The rules of grammar are written at a given point in time and space in the world. And even in that time and space, one might find that within a radius of several kilometres, or even several hundred kilometres, there are marked cultural and language differences which reinforce that often such "rules" are written by and for the benefit of the reigning middle and upper classes, and have little relevance to the working man's use of language.