They probably didn't know Seth was seriously hurt and could no longer perform as champion until after the fact.
That's not the point. He was vulnerable and it was in Dublin. No, they didn't plan for this to happen, but you can't ask for a better solution. The title is now vacated if we are going with your argument of them not knowing. Which I feel is a solid argument on your behalf. I still think Sheamus cashing in on Seth there on the spot, or while the title was vacated shortly thereafter in Ireland makes the most sense. Hold a huge press conference and The Authority there with HHH. Basically as someone said earlier HHH would throw Seth under the bus and talk up Sheamus as taking the opportunity and running with it. It's a story that tells itself and happens by accident. This goes to show how awful main roster booking actually is when something by accident can make more sense than something planned for 8 weeks.
Because it was a house show & it would make no sense to waste a mitb cash in at a house show. House shows also don't follow WWE canon so they'd also have to explain why Rollins was facing Kane.
People already know that Rollins was facing Kane. The fans in attendance and everyone that knows about the injury. There is footage. Kayfabe is dying. Haven't you heard? The title is vacant. Why hold a tournament when someone can just cash in. There is no rule about it stating that the cash in can only happen when there is a title holder.