Fiat currency and Bitcoin Both have their own and significant role, you can't say one of it is valueless. Currently both are playing a good role in our daily life.
Conclusion
It's true that people use fiat currency to trade Bitcoin. So, what do you want to use instead of fiat? It is very much normal that people use their fiat to trade valuable asset like Diamond, Gold etc.
Could it be possible to get bitcoin a value if not because of Fiat currency?
Could fiat currency will have no value without bitcoin? (Honestly fiat currency has value with or without bitcoin)
Why not? every valuable asset has its own value, somehow if you don't have fiat then it will be difficult to measure the value of that asset but it is not like that your asset will turned into valueless without fiat. if you want to sell your gold to someone who doesn't have fiat then he has to give you something else valuable thing to acquire your Gold.
* "You can have bitcoin but if it is not being tradable to fiat currency then your bitcoin has no value at all."- Your thinking is wrong, without fiat Silver,Gold,Iron has their own demand and value. People are gaining and earn BTC and spend that for taking service or fiat.
* "You need to buy bitcoin with fiat currency without fiat currency you can't have bitcoin"- Miner earned Bitcoin by mining, we earned Bitcoin in this forum by doing task and giving service,
Buyer or manager spend their BTC on us by taking service from us. Thus how Digital currency perform its work.
So BTC is a Self-contained Digital currency.
* "when you buy bitcoin you have to pay services like in those banks and when you like to convert bitcoin to fiat and withdraw it to a banks then you will then again to pay the service of the bank. You need also to pay the bitcoin transaction fee. So fees are everywhere from those banks to bitcoin network deducted by the miners."- This is a so-called fees, you are taking the best service with a little amount of fees without dealing with middleman and any kind of harassment.