In just about any competitive ladder for a particular game, a pause feature is included to assist situations where real-world factors impact your ranked games. Since Overwatch's inception, however, (a game Blizzard heavily pushed and set to establish an esports scene in) a pause function has not been implemented.
A five versus six situation and having to deal with the general team-wide morale loss of having a leaver calls for a bad time - it's clear why players want this feature added.
The Overwatch developers have come out and said their piece on why there aren't any pauses or backfills put into place for Competitive to combat leavers or disconnects. When replying to a question in a developer Reddit AMA on the Overwatch Subreddit, Principal Designer Scott Mercer explained the team's reasoning.
"There's no backfilling because we're pretty sure no one would want to do it... If we allowed players to backfill without consequences to their SR, its giving them a license to throw or act negatively." Mercer expects a backfilling feature would very likely get exploited, creating a greater negative experience to a ranked lobby that was already doomed to begin with if people are looking to backfill.
When answering the user on pauses, here is what Mercer has to say: "...we have to consider cases where players might abuse the rules in an attempt to harass someone or waste people's time. The best way to try and minimize leaves is to not provide any kind of outside motivation for them to occur."
It's always refreshing to see developers directly answer questions to the people. Small things like AMAs mean A LOT to the communities, even if it doesn't seem like it. It helps the player base realize that the developers behind their favorite games are not soulless husks of men and women who make it their duty to ruin the game - because that's not the case!