It's about concentration of power and distance of the represented from their representatives and it goes back to the Federalist and Anti-Federalist Papers. It's easy to forget that it took a lot of compromise to get the individual states to join together as one national state.

Look at our latest presidential election. Trump won huge swaths of rural areas where people felt that no one in either party gave a crap about their concerns. Without considering whether they were right or wrong about who they chose as their representative, it's pretty clear that the thoughts, beliefs, and concerns of a homemaker in rural Idaho are fairly different from those of a venture capitalist or graphic designer living in San Francisco or New York City. That divide doesn't seem to be getting smaller, but populations, and therefore power, are shifting more and more to urban areas, leaving those in rural areas feeling ever more alienated from their leadership. With the kind of robust separation of powers guaranteed by the 10th Amendment, this shouldn't be as big a deal as it is, since states would have considerably more impact on citizens' lives than the Federal Government. However, over the years the autonomy of the states has decreased and the power of the Federal Government has increased.

So, having said all that...you're exactly right that a larger organization such as the Federal Government has considerably more bargaining power than state or local governments and that could be used to save taxpayers money. However, just as we see corruption in large corporations we would most assuredly see corruption in the awarding of government contracts. These contracts would now be so large that they could make or break entire corporations, putting tens of thousands of people out of work if one of them shifted. Of course, there's a ton of corruption in local government as well, but its scale is smaller and people are able to watch their local representatives more closely.

That's probably a heck of a lot more than you were looking for, but hopefully it explains at least some of the reasoning behind the conservative aversion to federalizing all government purchasing.