TLDR: Leaving bitcoin on exchanges helps their clients (mainly institutional) to take short positions on bitcoin (depressing its price) as your bitcoins act as collateral for their trades. If they eventually go bust hard, you will/may pay for their loss.
Many people are wondering why the bitcoin price is not going up despite massive institutional buying and increased adoption. An important reason for that is that bitcoin seems to be suffering from a similar phenomenon (although in a much lower scale at this point) that gold suffers: The reason why gold is stagnated for years is because there are massive short positions kept by a few key players, which are “subsidized” by a vast amount of “paper gold” in the markets. With bitcoin, this happens through the exchanges.
People that care about the bitcoin price should stop using exchanges as wallets immediately. It does not matter that they are safe. They can be 100% safe, insured if you would like, just like your bank deposits. Bitcoins in exchanges aren’t “bitcoin”, they are “paper bitcoin”. They are a liability for the exchange and an asset for you, but a different asset than if you had the bitcoin in a personal wallet. What you have is a promise from the exchange to have that bitcoins deposited in an address you give should you request a withdraw. Under normal circumstances, this works well. Under distress situations, it does not. What the exchange has is a promise to pay you back, but only if they can. In many instances, they will not be able to. And that’s fine, they are limited liability companies. I am confident that the open short interest in bitcoin is substantially large, potentially much bigger than the number of existing bitcoins, or the bitcoin "free float". These short positions are collateralized by bitcoins left in exchanges, regardless if the exchange mentions it explicit or not. Some exchanges are honest and mention it clearly in their terms that in the situation where their insurance fund is depleted, losses will be socialized among winning traders. Others don’t. The bitcoins that you leave in exchanges are used as collateral, explicitly or implicitly, by them to finance short positions of their clients. Even if an exchange does not allow margin trading for retail clients, they very likely do for institutional clients, which is even worse. Notice also that it does not matter if the balance of clients matches what these exchanges have in their wallets. It is practically invisible to outsiders how much institutional clients are leveraged through these exchanges, and a way of estimating or getting a sense of it must be urgently developed for a better understanding of the market. If all those keeping bitcoins at exchanges withdraw them to a private wallet, the exchanges will have to increase their margin requirements for leveraged clients (or reduce the leverage limits), which will force these clients to close their positions or buy more bitcoin. There is no other way, and this of course is good for bitcoin. If people however keep using exchanges as wallets, then we run the risk of bitcoin being constantly manipulated by players who are able to leverage short positions at levels that we cannot even assess.
My recommendation is that those interested in higher bitcoin prices to move their bitcoin to addresses that they, and only they, have control of. This includes those likely making use of custodial services, particularly when custody is made by an exchange. It is quite ironic that many of these investors that buy bitcoin instead of gold because “gold price is manipulated by the banks” do exactly the same gold investors do. If you buy bitcoin to leave it deposited somewhere else under a custodian, particularly if this custodian has clients that can short bitcoin, you are very likely doing a disservice for bitcoin. Move your bitcoins immediately somewhere else, buy insurance if necessary, or leave them with a custodian that performs only custody and nothing else. The reason by the way why custodian services are usually cheaper than insurance is precisely because the custodian can profit on you (by having your precious bitcoins in custody) in other ways.
As long as we have bitcoins being left in exchanges or in the hands of custodians that fill very much the role of the same banks that bitcoin holders aim to be disconnected from, we will have bitcoin moving sideways and fighting hard for higher price levels.
In the end, inevitably, bitcoin prices will grow. But this process can be much faster if each bitcoin holder takes care of its own bitcoins or leave them with true custodians, not exchanges.