I do not have any basis to say that there is some thing fundamentally wrong at HDFC Bank.
This statement of yours was very honest and was also enough to close the discussion 
But nonetheless your state of mind is a reality many people face even I do (in other contexts) and, therefore, it’s important for us to know how to deal with this mindset which brings uneasiness. Not that I am any authority on the subject but am just taking liberty of this being a social media platform to share my experience
The points you have raised are mere possibilities and since investing isn’t based of possibility of outcomes but probability of outcomes, it’s important we evaluate each possible event in terms of probability.
Here for all the points you have mentioned the probability is very low, solely based on the track record of the bank and the person and it is this track record which if “studied well (not necessarily studied deeply)” will tell you why the two are in a league of their own.
Just bcoz past performance has been extraordinary doesn’t mean it was cooked up. In the context of hdfc operating in the indian banking industry it was like a well-disciplined, intelligent and self-assured person looking at a sumptuous 7-course meal every day but choosing to stick to a disciplined diet even when many around him went on a binging spree. So a 20% or 30% consistent growth could well have been by design maybe because the opportunity was so large that you could decide how much “you want to grow”.
People like Abhay, Munish, etc leaving was pretty candidly addressed by AP during the last call. But yeah, there are many who wud choose to brush it aside as corporate speal!! They were highly experienced, intelligent, hard working people of high integrity (based on my limited knowledge after seeing some of there interviews, presentations and work over many years). They would have also inspired many in their teams to fill their shoes. To link them to any kind of clean up exercise is a low probability event, for me.
Auto loans issue is something which is an isolated bad event and I wud assume it will only make hdfc bk stronger as they take measures to ensure the possibility of such issues happening goes down.
And as much as one can say that the continuity of past performance is baked into the price it is equally debatable that the “best bank ever” has been beaten a little too much to be trading at decadal low valuations and that this opportunity won’t last long!!
A change at the top means clean up, is also just an assumption which becomes weak the more you “know” the bank and the person. Stricter RBI regulations (AQRs, etc) also help making the overall environment more complaint. Still bank’s asset quality hasn’t changed much. Also, if hdfc has been a high quality bank in India and for a long time then probability is also high that it will also have the high quality borrowers thereby reducing the probability of possible clean ups. Quite frankly, for me, clean up happening at hdfc bk post AP is akeen to conspiracy theories we read all the time on web these days And yet I don’t negate it fully but just put it way below in terms of probability.
RBI dragging its foot on selection: I would assume these are tough times for RBI, very tough. If I was rbi gov I wud even explore the possibility of extending AP’s tenure by maybe a few months allowing RBI to focus on far more important issues at hand. In these times approving top level changes at a bank which has long been the flag bearer of Prudence and Growth in Indian Banking, can’t be taken in haste.
And yes there is always a fear that a great manager is going and so performance could fall but “it is just a fear“ and we need to work on it ourselves if we want to overcome this fear.
Hdfc bk would still tick almost all the boxes for it to be seen as the best bank in India even after he is gone.
So, in the end, there is no denying the fact that Aditya Puri was a great manager. And it isn’t that it doesn’t matter that he is leaving, what matters more is what he is leaving behind!!
