There are very few cases where I actually want tabs running in the background, and I'd be happy to add those cases to a whitelist in exchange for Chrome not eating my computer.
But as long as no browser does that, OP's option looks like a huge timesaver for me.
If something like that was implemented, I would hope that it would be turned off by default and hidden away under the "here be dragons" section of Chrome's settings.
But as long as no browser does that, OP's option looks like a huge timesaver for me.