The assumption is that the CPI is what it is. It's external, independent, and stable. Therefore it's an unbiased way of doing things like adjusting Social Security.
As soon as it's used to adjust Social Security, then there's an interest in making sure the CPI serves the interest of those who are involved in Social Security. "I need a bigger increase, but the CPI is 0.1%? That's not fair!" Or, "The SS Trust fund will run out in '35, if we do something to reduce the CPI then it'll last longer. We must do something to reduce the CPI."
The more that rides on the CPI, the worst the desire to manipulate the CPI will get.
It's like Congress. We've had lobbyists besieging Congress for nearly 200 years. But that's only a small part of the picture. They were often sent for specific purposes, for limited times, and weren't numerous or important. They'd show up, do their jobs, and go home. Or a firm would have a lot of short-term, small customers. It was with the increase of Congress' importance in handing out a lot of money, managing the rules that businesses live by, extending its influence that we saw a big upsurge in lobbyists. The stakes were higher, both in getting larger contracts and controlling the regulations that you (and your competition) had to work under. All kinds of things that hadn't been political were suddenly political. And subject to Congressional manipulation and corruption. If there's more power to buy, there'll be more people in the market for buying power.