You are right, of course; the only thing I have to add to your observations is that 'Keshavananda Bharati' laid down a very, very broad foundation, that only said that the 'basic structure' of the Constitution could not be affected, but avoided the question of what that 'basic structure' was; you will find that the Mangaldas & Mangaldas (or whatever this branch of the split partnership calls itself now) blog gives some detail about some of the opinions. It was a 12 judge bench, and there were 11 individual, separate judgements! Finally Sikri J. had to summarise their views into a 'View of the Majority' precis with 6 propositions in it. The broadest view was that of Khanna J., who said that amendment meant changing a part, therefore there must be a whole, therefore amendment cannot alter the nature of the whole. Subtle, very subtle; also minimalist, nothing added that isn't there visible in the broad glare of daylight. In view of his later political history, this view has a delicious irony to it.
It was only subsequent judgements that elaborated on this basic proposition. How it did so is an exercise by itself; only hard core constitutional lawyers will be interested, and I would like to spare you the burden of wading through them (they are all mentioned under that URL).
How did the pols react?
Furious! Read for yourself. All hell broke loose after 'Golak Nath'. Indira packed the bench, put in a stooge as CJI, who put together another (13 judge) bench to review Golak Nath, and that fell apart in disarray, when it was discovered that the hearing was baseless - NOBODY HAD FILED A REVIEW PETITION!
The Bench was dissolved, the review was thankfully abandoned, the CJI in question permanently lost his reputation and became known as a sycophantic lickspittle, and the Court pieced together its views on the basic structure judgement by judgement.
(You might be interested to know that, after the Shah Bano case, where the political abandonment of women's rights in favour of the blackmailing, bullying view of the self-certified Muslim Personal Law Board was embodied in parliament passing a law to that effect, the courts fought back and implemented the law such that women got the very most that they might have hoped for under this inequitable law).
No politician or political party liked the judgement. They reacted very badly.