On the contrary:
It's not sportsmanlike to start a tourney game, save it and come back hours or days later while ev1 else waits for the player. This would be possible from your proposal.
For the sake of the community, there must be a fixed end of the tourney. It belongs to the duties of the players to obey to these limits. Thus you killed your round yourself.
Edit: Even more in a RG. If you choose to wait till the last second it's all up to you.
Everybody knows (or should know) when the weeklies/monthlies end, it's 11:59 pm PST.
The timing for RGs and CC tournaments is indicated in the tournament section of the game client.
And, BTW, the time may have been elapsed before. The program only looks at the clock on the last stroke.