My research and thus opinion is that business analytics is most certainly an organizational strategic function. If IT, Finance, HRD, etc. are considered strategic functions of an organization, so should the Analytics as well.
As someone who has worked in IT for over 30 years, I basically agree with much of the role of IT as you have decribed previously. However; placing one "strategic" function under or within another diminishes the impact that analytics can have on an organization and allows it to compete for resources with other important things.
As far as putting the analytics function out into the organization business community and expecting those folks to become "data scientist" is probably, in most cases, not feasable if one understands what the skillset and role of a true data scientist is. Its not that standard business users can't use business intelligence and analysis tools to perfrom basic analytical functions, data scientist have different backgrounds, training and experience when it comes to the quantitative side of analytics.
Assuming that an organization is fairly significant in size, the proverbial "make everyone a data scientist" concept is probably not practical for many reasons. My concept which is not new or uncommon would be to establish a center for analytics excellence separately from IT and the business units and staff it appropriately so that the organization can focus on solving the most complex business problems. For obvious reasons, they would work very closely with IT and the business units, however; they would have separate priorities derived specifcally from the C-suite or senior organizational leaders. Otherwise the chances of realizing the true value and recieving the maximum benefit from your data may be far reaching from a strategic planning and organizational standpoint. Just my rambling thoughts....