It wouldn't be stopped every tackle though. If it was limited to huge, match changing plays then I really can't see a problem.
At the end of the day, our opinion is based on how it would change "the game we watch." Players may have a different view, I imagine no one would have minded if Fabio Capello had the ability to challenge the ruling of 'no goal' after Lampard's strike vs. Germany in 2010. It would take no more than thirty seconds to change the ruling to a goal. The game then kicks off again...
So what? The game we're accustomed to watching pauses at maximum six times in a game, for no more than a minute a turn? I'm sure some players would have a completely different view away from the interest of entertainment and viewing pleasure.
Goal line technology is a bit different as it doesn't require a stoppage, the result's near instant. I've got no problem with this.
But for video replays, limiting it to huge match changing plays isn't something I could ever see happening, do you say if a goal came in the next 10 seconds we'll look at it again? Every tackle in the box in case it was a pen? How do you say when you're gonna blow the whistle to take a look?
Or if you're not blowing the whistle and have a seperate video ref looking at replays who can pull play back, you're gonna have a lot of time getting played that "didn't really count" (purely because why would the ref blow when the video ref will be more accurate, he'd be a mug to risk the wrong decision so anything other than a dead cert he'd leave upstairs).
I'd love for the game to be totally fair and still fun to watch, but I can't imagine making it stop start would keep it entertaining.