Even if the fees will be 1/2 or even 1/4 from what they are now they would still be too high for daily usage. Imagine you would have to pay 5-10 bucks every time you buy something with your credit card. I don't think Segwit and LN would decrease the fees to less than 1 USD, so even if bitcoin sustains, there is surely a room of alts to take over in areas where using BTC will simply not be worth it.
1USD fee would solve a lot of problems, now I agree that you won't use your Bitcoin on a daily basis to buy "many stuff" but don't worry, I don't think Bitcoin was ever invented to be a daily life payment solution. Fiat currencies won't disappear, but even if Bitcoin is used in 10% of all transactions in the US for instance, the price would reach at least 100k USD, and it is not out of the realm of possibilities in the next 5 years if everything goes well.