Why?
If everyone uses litecoin why would Bitcoin be better for larger transactions?
If *everyone* uses litecoin, it won't be.
The chances of that happening is near zero for a long list of reasons.
What will happen, at most, is that shitcoins will be used for low-value txs and btc will be used for high value txs. You want to gamble for a few cents => you use a shitcoin. You want to buy a chewing gum => you use a shitcoin. You want to transfer 500$ or $5 mn, you use BTC.
You are advancing a hypothesis as a known. I think your hypothesis is faulty.
I believe that, should any alt be adopted for small value transactions, the line between 'small value' and 'large value' will quickly trend upwards in absolute value, eventually subsuming all of the actual value within the so-called 'high value' transaction space. If indeed this vision is correct, the Bitcoin would be left eventually as valueless.
The fee market dictates the transaction type. If you have, say, 1$ fee, you can't perform 1-2-3$ txs. You can however perform 50-100-1000-1mn USD txs.
When you have a network that does like 500.000 txs of an average 1.000-10.000$ (acting like the "SWIFT" of crypto), you are at 0.5 to 5bn USD per day.
And if you have a network that does 10 times the number of transactions, say 5mn txs, but for "small" values, like an average of 1 to 10$ per tx, it will only be at 5 to 50mn USD tx volume.
One would say "but why wouldn't people keep their money on the second coin with the many txs etc". The answer is: because it is a disposable coin / a joke coin, that will be unable to preserve functionality in the long run.
It is impossible for a low-fee coin to survive blockchain abuse, which, in the long run, will render that coin unusable. If there is no new mechanism that allows for scaling, all the reasons that prevent bitcoin from going into huge blocks are also there. And they are exploitable. Imagine you have an altcoin that tomorrow gets all the btc load for near zero fees. What's stopping script kiddies from inserting tonz of transactions for the lulz to see the network get clogged? And then people will say
"oh fuck that, I came to this altcoin to escape higher fees and now I'm queued for ages and I have to pay fees again, and then, as the attackers are willing to pay even very small fees, I must now pay even higher fees, etc, etc... it's all fucked up". LTC, DOGE are affected in the same way. We'll see how DASH goes because it actually will try to do something different, through the masternode network, but anyway. If you can get many txs for free you can also spam for free and abuse the system (and then the devs will have to "react" by increasing fees to stop the abuse, etc etc). Monero got attacked that way last year I think, and they had to raise fees to prevent the blockchain from getting bloated to DOA levels.
At MOST, some people or group could sink billions into an altcoin, complete with incentives for miners to switch, a well-funded marketing effort, a competent development group that they can control (or at least trust), legal defense fund, lobbying team, focus groups, etc.
What's seven billion dollars to Wall Street or Silicone Valley? What's the payoff if they succeed? I'm surprised they haven't done this already.
If that altcoin has very low or near zero fees, it will be exploitable - no matter who creates it. Btw, the scenario of a Wall-Street-coin or Silicon-Valley-coin, is not a real threat due to being centralized. As I told you yesterday, these will be competing in the centralized space with visa and paypal, not with BTC.
If they are an alternative player with a decentralized currency and they arrive on the scene claiming that they can supply millions of txs for free, I can make a script to add gigabytes per day for the lolz into its blockchain. At some point, when people will not be happy with this, and the network will be threatened for its long-term sustainability, the devs will have to "react" and raise fees in order to prevent me from spamming it.
Big money will not necessarily solve the scaling issue. Code will (scaling improvements, new compression algorithms, etc). Or technology will (more storage, faster processing, greater bandwidth etc). Things that apply today, in terms of technological restrictions, might not apply in 3-5-10-15 years. But even if you have a far more capable network in terms of tx capacity, it will always be subject to abuse in a zero to low fee scenario. And thus it will need to be protected. This applies to both BTC and altcoins.