Litecoin to me is useful and valuable to me in a lot of ways.
1. Diversification of one's cryptocoin portfolio. 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.
I'm not holding crypto-currencies because I'm investing, but because I think they're a good idea to conduct transactions over the internet. I bought a set of such currencies (Bitcoins, Litecoins) a long time before all of the hype (see the creation date of my user account, started buying Bitcoins well before I created the account) and I didn't really expect them to rise in value that much. "Investing" in currencies is just stupid, because that's basically a Ponzi-scheme. That's even true for Bitcoin to a given degree now, but at least there you have actual usage of the protocol to offset the speculation. If you want to "invest" in something invest in Bitcoin/Litecoin related companies instead of bubbles.
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.
That's only a very temporary advantage. While Scrypt has the advantage that it is "memory-hard", technology changes still have the same effect on Litecoin as on Bitcoin (and other cryptocurrencies). Once ASICs are the primary hashing technology in the Bitcoin world it's hard for adversaries to come up with more effective solutions (unless they can spend lots of energy). With Scrypt on the other hand you'll be facing the same problems, but just at a later time. And the attack described by you above would also be possible against Scrypt, as you could use a Botnet instead of an ASIC for this. OTOH, once ASICs are the standard in the Bitcoin world Botnet attacks aren't feasible at all, as the hashing rate that can be reached with them is much lower than what a few ASICs deliver.
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.
Visa and Mastercard are different technologies, but they still use a commonly agreed on currency. You already have that in the Bitcoin world: A common currency and dozens of different client implementations. You don't have that in the Litecoin world - there you can only choose one from two outdated and unmaintained clients.
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.
Waiting for 6 transactions (or whatever) is just an arbitrary number. You correctly noticed that the same transaction amount for Litecoins is less secure than for Bitcoins. So why not just wait for less transactions when using Bitcoins?
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.
The only reason why the community grows is because previous Bitcoin miners find out that there equipment is suddenly useless and therefore try to earn money with Litecoins instead. The fallacy here is that miners don't really matter much when it comes to the utility of a currency. The community that would need to grow are the actual users conducting transactions via Litecoin and this community is still extremely tiny.
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.
So you say that Litecoin is a classical bubble? People just buy it because they assume that its value will rise?
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?
The exchange rate is just an arbitrary number and doesn't affect real-life utility. The Zimbabwean dollar is not a better currency than the US dollar, just because you need billions of them in your pocket to buy a breakfast. But if there's really a psychological reason behind this it might be time for the Bitcoin community to switch to mBTC or all the way to Satoshis as currency unit.
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.
In practice (if you look at the source code) Litecoin is basically a copy of an old Bitcoin version and has not been updated for a very long time. In other words: Almost all of the attacks applicable against Bitcoin are also applicable against Litecoin. In addition, all the security issues that have been long fixed in the Bitcoin have been mostly ignored by Litecoin (so Litecoin is still vulnerable to them). Litecoin users are claiming that Litecoin is "more modern" than Bitcoin, but the truth is that it is basically outdated and unmaintained.