In an interview I read with Steve, he said that Jim mentioned to him that he'd always regretted that Steve hadn't been given a more prominent regular character on the show (meaning that Jim didn't feel that Rizzo was of the same caliber as Fozzie or Scooter), and wanted to meet with Steve to discuss fixing the situation. The meeting never occured due to Jim's passing, but soon after that, Steve was given Kermit to perform. Steve said (and I'm paraphrasing) he'd never dreamed that this was the regular character Jim had in mind for him.
I know that in the beginning, many people naturally assumed that Brian Henson had taken over Kermit after Jim's passing. Around that same time, veteran voice actor Mel Blanc died, and he had announced two years earlier during the production of Who Framed Roger Rabbit that his son Noel would take over the voicing duties of Bugs Bunny after Mel passed on. This led to the assumption that every son of a famous voice actor or puppeteer would take the reins from his deceased father. Ironically, Noel Blanc didn't end up voicing Bugs Bunny ever, and a succession of voice actors have done the jobs ever since.
I believe Brian felt he couldn't perform Kermit because of the powerful bond the character had to his father, so giving Kermit to Steve was not only the best choice, but probably a necessity.