What will happen when only large institutions can afford to use Bitcoin's blockchain, due to rising fees? Won't this centralize the network if most can only trade bitcoin on centralized exchanges?
You are missing things together but let's de-concatenate your questions and discuss them one after the other.
When large institutional investors use Bitcoin blockchain to make transactions, it will lead to more unconfirmed transaction in the mempool waiting for miners to mine them or include them into the next block and in the case where the mempool get congested, the institutional investors and everyother that make transactions will have to pay a higher fees before their transaction can get included into the next available block for transaction to be go comfirm.
There is no way this makes the transaction to be centralized, transaction on blockchain can never be centralized but if the institutional investors make use of centralized exchanges to trade it still doesn't make bitcoin centralize. The bitcoin centralization and power lies between the miners, the node and the Bitcoin protocol. This is impossible and can't be done to Bitcoin.
What if the exchange also runs a mining pool
