As @coblee stated back in 2014:
What does Litecoin have to gain?
When coins have to compete for miners, someone always loses. As Scrypt ASICs come on the scene, the “there can be only one” theory might turn out to be true for Scrypt coins. Given Litecoin’s dominating hashrate and Dogecoin’s mining flaw, it is likely that Litecoin will keeps its #1 position (Scrypt). That said, there is still a small chance that Litecoin will lose out to Dogecoin. Merged mining eliminates that possibility by making it so that each coin can thrive on its own merits and not have to compete for miners to survive. By combining mining hashrate, both networks become stronger. It’s a win/win for both coins.
Most of the Litecoin supporters, I’ve talked to, think that I’m wasting my time. Some want Dogecoin to die and don’t want me to help Dogecoin and let it’s mining flaw kill it. Some think that they will not appreciate my help and/or will end up not doing it anyways, so it’s a waste of my time. Some think that by helping Dogecoin now, I will actually give them a chance to survive this and eventually overtake Litecoin.
So why am I doing this? I’m doing this because I believe Dogecoin is good for crypto-currency. It started as a joke, but now it’s no longer a joke. It has brought a lot of users into crypto-currency that would otherwise not be interested in. I think that’s good for crypto-currency and good for everyone involved. I think there’s room for many crypt-currencies to thrive. And if a 51% really ends up killing Dogecoin, a lot of users will be hurt. That will turn off a lot of users from Bitcoin and Litecoin. And that’s bad for the whole movement.
Except from https://www.reddit.com/r/dogecoin/comments/22niq9/merged_mining_amafaq/