From what I understand based on Colbert's monologue, their motivations for suspending Kimmel is completely monetary based. ABC affiliate company Nexstar made a $6.2 billion deal to acquire TEGNA Inc and Disney which owns ABC made a deal to get some NFL assets in exchange for a 10% stake in ESPN (valued at around $3 billion).

Both of these acquisitions will need FCC approval to go through. Take a guess at what they're willing to do to get that approval.