If you think that 60 GH/s is a lot for an ASIC, then think again.
Crashing Dogecoin would do no harm to other cryptos, that's nonsense.
60 Gh/s IS a lot for scrypt asics. I am not saying that it is impossible to crash Doge, I am saying that anyone who invested enough money to do so would not spend it trying to disrupt the network. Not even for the lulz.
Secondly, when people reference the possibility of a 51% attack, they reference incidents like Feathercoin. A double spend attack on one moderate sized coin caused concern even in larger coins. Not enough to lose faith in them, no; but the fact that it is cited is enough.
In the future, when more of the general public becomes interested in Bitcoin, they would hear about a coin as large as Doge being attacked, and question if something even as powerful as Bitcoin is worth the risk.