Litecoin to me is useful and valuable to me in a lot of ways.
1. Diversification of one's crypto coin portfolio. You already mentioned this, so I won't elaborate too much, but someone such as myself that really likes Bitcoin can use other crypto currencies to diversify their crypto portfolio (this valuable trait is not specific to Litecoin.) Age old investing ideology comes into play here and this is just smart investing. Only investing in Bitcoin is like going all in on Google stock.
2. Litecoin being built upon Scrypt makes it stronger than most other ALT currencies, especially the ones that are SHA-256 based. If you look into the problems TRC is facing, you will see that ASICs are hoping on their chain and sending difficulty into the stratosphere. They then go to hash something else, leaving the TRC block chain moving at a snail's pace and transactions taking hours to days to confirm. All SHA-256 based ALT coins (that do not have Scrypt) will suffer from this problem until they are fixed.
3. Litecoin is useful to the crypto currency ecosystem in the way that it's useful to have Visa, MasterCard, and Discover Card... or Wells Fargo, Bank Of America, and Chase. Sure, they all do the same thing, but they all do the same thing a little bit differently. Also, if one were to fail, there are others in existance so all commerce would not screech to a halt across the nation. It is good for Bitcoin to have a competing entity that is similar but not the exact same to itself. For the benefit of free market competition, each currency will always be striving to stay ahead or to catch up to one another, at the end of the day mutually improving both currencies by default.
4. Litecoin confirms in 1/4 the time that Bitcoin does. This one is brought up the most often for obvious reasons. I am sometimes impatient and do not want to wait 10 minutes to a hour+ for one or ten confirmations on the Bitcoin block chain. Although in theory this makes Litecoin 1/4 as secure as Bitcoin, I personally have never suffered any problems using Litecoin. Also, Bitcoiners refute this point by stating Bitcoin will soon be faster as soon as the devs increase the block size (I think this is the method they are trying to use), but it is a lot easier said than done. If it was an easy thing to do, then it would have been done long ago. Litecoin is faster right at this moment, which is valuable to me.
5. Because blocks are found 4x faster, difficulty adjusts more quickly.. about every 3.5 days. This is useful because it controls the rate of the minting of Litecoins, and makes sure that they stay provably scarce for some time to come. Again, this is valuable because it stabilizes the network and deters high powered hashers from shooting difficulty into the sky and then leaving the network at a crawling pace for a longer period of time (than if blocks were solved at the same pace as Bitcoin.) This feature is not all butterflies and fairy tales, it also provides the opportunity to manipulate network speed, but as the network grows this will become less and less of a problem.
6. Then there is the "there's nothing to do with your Litecoins" fallacy. These people just don't do their research, there are plenty of things you can do and buy with Litecoin as of this instant. New merchants and services are popping up everyday, and I think this will continue to happen well into the future.
7. The Litecoin community is growing at an exponential rate. Similar to the growth of Bitcoin, as the community grows then so will Litecoin. Litecoin is already far too big and the people that believe in it are too invested in Litecoin for it to fail at this point. Litecoin can at this point proudly say that they are king of the ALT coins. It can no longer be brushed aside as a scam/pump and dump/whatever, it has real value and people are starting to see that.
8. Like Bitcoin, there was no Litecoin pre mine. There was the genesis block, and 2 blocks to confirm the genesis. This is valuable for obvious reasons... no one wants to support scammers, and for a crypto currency to become highly adopted this is a necessary feature.
9. Not everyone was so lucky to be around when Bitcoin was first started and able to buy them for pennies. The possibility of becoming an "early adopter" is very appealing to new crypto currency users. A ton of "noobs" have recently appeared in the last wave of Bitcoin mania and I've noticed that a lot of them overwhelmingly support and/or already use Litecoins.
10. As Bitcoins become more valuable over time, this will further push the poor and "working class" away from it. Some can no longer afford to buy one Bitcoin even at today's prices. People like to get more for their money, and when buying at today's exchange rate people can get more Litecoins than Bitcoins. If the same services and merchants start accepting Litecoins, then what is the purpose of paying $100+, $200+, or $300+ per bitcoin?
11. Litecoin has the advantage of doing everything after Bitcoin. By sitting and waiting in the shadows for people to bring to light exploits and bugs on Bitcoin, these problems can be fixed before there is much of a problem or before someone exploits it. Bitcoin would obviously be exploited first if there was something to exploit, because of the bigger market cap and it is more valuable for someone to exploit Bitcoin first rather than Litecoin.
12. Litecoin derives its value in the same way that Bitcoin does. It is provably scarce and its value is held up by supply and demand. Bitcoin had proven that this in itself can hold up an economy and even make it thrive. As long as there are new services and merchants accepting Litecoin (as there are), then demand should not go away. And... we all know by now that supply stays constant, thus giving Litecoin value.
13. It's anonymous.