I like the concept, however it may not be very useful to people who only want to play ranked because you would certainly only be able to play a casual match afterwards. I don't think they would implement a feature that lets you bypass matchmaking.
Having a rematch is a nice idea - however the idea of it being intentionally "hostile" doesn't really sit very well. HS is already struggling with flaming and salty players after a match. I don't think Blizzard would want to encourage that sort of feeling between players.
Such a terrible idea, Blizzard would never do something like this. Why? Because they would never admit they promote BMing in any way. Don't you know how people react to this things, OP? Seriously, do you live under a rock or what? This would be one of the worst decisions Team 5 could ever make considering their target audience at the moment.
I think something along the lines of a "rematch" idea could be good. Sometimes you just want to have another shot because of RNG or draw or making a misplay and never recovering.
I'm not sure how it would work out if you're waiting for a rematch and they're playing a fatigue warrior build and take 30 minutes per game on average, but maybe creating a queue in which you can even choose to pony up rank or gold or arcane dust to incentivize your opponent could be a great way to balance out tilt. If you're willing to rematch that person AND put up something of value like 50-100 gold or 200 dust, you can't complain if they win again, because you literally bet that you could win. No blaming random matchmaking for that loss.
Also, obviously I think the mechanic should be limited to losing players. Winners don't need a second chance.
Lastly, I think a wager system between people on your friends list could be great, so long as Blizzard managed to keep players from playing themselves and using dummy accounts to store up gold/dust and purposefully lose it to their main account.
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Rage quitting: the best way to ensure your opponent knows they beat a giant baby.