Why did bands appearing on Letterman used to have to play along with the house band?

[installLSC]

@installLSC

I remember a Rolling Stone article from 1994 on the competition between Leno, Letterman, and Arsenio Hall for musical guests. It noted many acts were wary of going on Letterman because they were required/urged to used Paul’s band (I’ve forgot the exact wording, and the libraries are closed for the weekend).

I actually found the article. All it says about Paul’s band is “The old and unpopular practice of guests having to sit in with Paul Shaffer and the band as sidemen is ‘flexible’ now” according to Letterman’s booker. So still no clue as to why the rule was put in place, but at least we know it was an NBC era thing.