Music licensing deals made at the time of WKRP in Cincinnati's production/original run were or a limited number of years. The original licensing deals expired about several years after WKRP initially went into syndication shortly after its cancellation. After then, generic "sound-alike" replacement music had to be recorded by studio musicians to purposely avoid having to pay royalties to the artists whose songs were originally used on the series.

When Shout! Factory released the "Complete Series" set in late 2014, rights were obtained for songs by a majority of the artists whose music WKRP in Cincinnati used (around 111), and in some cases, it was simply impossible to get the rights for a few other songs.

If WKRP in Cincinnati were to be put on a digital platform like Hulu or Netflix, would the sitcom's distributors have to go through the process of acquiring new licenses for the music used on it all over again?

A series set in a radio station having to go through all that mumbo-jumbo...

I honestly don't think we'll ever see "WKRP in Cincinnati" on a digital platform. Hulu has Season 1 with the cruddy Fox release, BUT the one Shout released was exclusively for DVD and not streaming. Fox must've made a deal with Hulu and maybe Amazon Instant Video and iTunes for it to be included. But the deal with that the episodes' mater copies are in such bad shape as evidenced by the DVD set (some are not bad, even good, but certainly not sharp enough quality for what VOD services look for). Shout got ~90% of the original music, which is amazing considering the set currently retails for around ~$70 at times! And the fact that the licensing for the music was like that when Shout released it... I'd say it would never work.