The problem is not everyone wants turtling until late game to be an effective strategy. It makes games take a lot longer and allows the "winning" team to lose the game off of one mistake.
However the amount of damage turrets can take is not the problem, and does not really effect snowballing that much. Snowballing is mostly based on a general lack of opportunities for someone who is behind in certain lanes to catch up without outside assistance. This doesn't effect all levels of play, but the majority of players are effected by it.
The other problem is how much damage the turrets do. Sure, making the turrets tougher will slow things down, but it doesn't make towers a threat. That is what is currently missing; turrets are not a threat for the majority of a match. Even in the level 1-3 range top laners can often take a few accidental tower shots without it completely messing them up. Making towers tougher would definitely be something I'd like, but I'd rather they do more damage to champions first.