Fazlur Rahman's 'living sunnah' concept is just a sophisticated way of spinning the same old argument That the prophet left a series of practices out the Quran. Did he? Sure - if the Quran LIED to us.
The Quran is very clear that if the Prophet forged any other teachings after Quran (ba3dahu), he's be done for (69/40-47)
These living sunnah practices are nothing more than Pre-Quranic practices which are relabelled in order to make it seem that Quran approves of them. They say their kaabah is the quranic kaabah for example. How do we verify these claims? Context. Read Quran how it's arranged and we can see for ourselves, none of these practices are based on it.
Maybe the Ka'ba was pre Islam paganism. But the goal of the Quran is not to change those rituals as much as its to reform them into monotheism. There are many rituals of that kind in mankind history. To whom is the worship is the question.
Maybe Querish wanted to standardize these rituals as Islamic and binding, hence the need to attach either the prophet Muhammad or Abraham into them. But from a Quranic view, rituals are just rituals. they don't tell us anything. there are pagan rituals, and there are monotheist rituals. On the outside they may look the same, but to whom the ritual is dedicated to and to which deity its for, is the difference.
The Quran makes that clear when it always brings back the focus to faith and deeds. Rituals like pilgrimage and sacrificial rites are human functions very common throughout mankind history.
22.34. To every people did We appoint rites (of sacrifice), that they might celebrate the name of Allah over the sustenance He gave them from animals (fit for food). But your Allah is One Allah. submit then your wills to Him (in Islam) and give thou the good news to those who humble themselves,-
22.36-37 The sacrificial camels we have made for you as among the symbols from Allah. in them is (much) good for you then pronounce the name of Allah over them as they line up (for sacrifice) when they are down on their sides (after slaughter), eat ye thereof, and feed such as (beg not but) live in contentment, and such as beg with due humility thus have We made animals subject to you, that ye may be grateful. It is not their meat nor their blood, that reaches Allah. it is your piety that reaches Him He has thus made them subject to you, that ye may glorify Allah for His Guidance to you and proclaim the good news to all who do right.
So these rites are throughout mankind history and we see that in ancient religions. We see temples and ceremonies and sacrifices and rites. Usually to honor gods and to show thanks. But the Quran says these must be directed to God and not other gods. I see THAT as the goal of the Quran. So I am not sure that the Quran intended to come up with something new. But it did come up with monotheism and justice. Faith and deeds.