> Some rich states tried to procure vaccines on their own.
My point was that the states themselves asked to be allowed to procure the vaccines, so blaming the Union for asking them to "compete" is incorrect. As your link to the Liberalized policy states, 50% of the supply was being purchased by the Union, presumably to supply to the "poor" states.
> How does that preclude the Union from extending vaccine coverage to all?
You're right - it doesn't. However I think the (only) Rs. 35000 crore budget should have made it clear that the government was not planning to inoculate everyone for free. Some, like me, got lucky; but I know plenty of people who had to pay for their vaccines.
> And then placed an order for a grand total of 11 million doses
From Jan 16-Feb 28, India was inoculating only frontline workers and healthcare staff. For these AFAICT, the Union ordered 11 million vaccines in Jan[1], as you mentioned, and 14.5 million in Feb[2].
India started inoculating senior citizens and people with co-morbidities from March 1, and in March the Union had ordered 120 million vaccines[3].
The Union claimed, in May, that they were purchasing the entire supply of both SII and Bharat Biologicals, so if there was any shortage it was due to the lack of manufacturing and not lack of purchase. I'm not blaming the manufacturers of course - obviously they took time to scale, and they (especially SII) have done well now.
1. https://www.indiatoday.in/coronavirus-outbreak/story/india-o...
2. https://www.business-standard.com/article/current-affairs/go...
3. https://www.hindustantimes.com/india-news/120mn-doses-ordere...
Edit: added some more information on vaccine orders