They can charge very expensive withdrawal fees, for example.
Problems with Coinbase withdrawal fees.
They can freeze users funds.
[INFO] Updated Summary of malpractices and abuses of exchanges

They can ask KYC in your surprise.
OKX frozen my account and required me to KYC with a less than $1,000 deposit.

Things can change very quickly with centralized exchanges from their sides like policy changes, scam activation or by newest regulation and stricter enforcements by governments.

The risk is we as users never know what will do by centralized exchanges in coming hours or tomorrow. If people cannot afford to lose money after funding their accounts on centralized exchanges, they should avoid such centralized platforms.
Events made you scare about custodial wallets, centralized exchanges.

The exchanges that are shutting down were not that popular anymore or were being run poorly. As a holder this should mean nothing to you because we should know better than to use an exchange for long term holding. These exchanges shutting down aren’t a systemic risk the way FTX was when it collapsed.

Those reasons you have mentioned reminds people not to store their Bitcoins on any exchange, especially if they aim or decided to hold it for long term.

If it happens that those exchange decide to shutdown their operations. There's a possibilities that their users  may experience either balance losses or experience lots of stress due to withdrawal delays.

So treat exchange as trading platform only and not a storage to hide their Bitcoins. The safest and ideal option to use is the non custodial wallets, because they are the one have control on their keys.

Like what OP has given as the situation, there are long term bitcoin holders who have confidence to keep their bitcoins on exchanges. They're in that situation that what if an exchange collapses and they are no given prior notice because they're hacked or their funds have been siphoned and ran by the owners. Those type of situations will have to make those who continue to keep their funds in exchanges. They'll learn things and lessons in the hardest and most expensive ways if they'll never take these things seriously and never change their habit of how to keep their funds in their custody.

Both BitMart and BitMEX have been around in the market for a long time. BitMEX was founded in 2014, which means it's been around for 12 year now. BitMart is relatively newer, having been founded in 2017, but it has also been operating in the market for almost a decade. So i'm a bit surprised if you say you saw this coming.

Moreover, both of them clearly announced their closures and allowed users to withdraw their fund before ceasing operations, instead of suddenly collapsing like FTX.

So far, there haven't been any reported user losses, although there have been some report of withdrawal delays. So we shouldn't lump all of these cases together.

Exchanges are not reliable or safe for keeping bitcoin, and the first reason for this is that they do not meet the security standards for bitcoin investors: "not your keys, not your coin." An exchange can be reputable, but you don't know what may happen to it in the future, and this is why keeping bitcoin on an exchange is not advisable. There are many reasons why exchanges end up crashing, and one should not rely on just one.
Exchange is not meant for keeping bitcoin; exchange is a place where bitcoin is traded "buy & sell." If exchanges are shutting down, I don't expect people to be worried about where to keep their bitcoin, and if people should be worried about the shutdown of exchanges, it should be because of buying or selling. A non-custodial wallet is the right place to keep bitcoin because this gives one full ownership and control of one's assets.

We do not know why some exchange are exiting, they are in good position to anwer any question to that effect, however, For Bitcoin investors whose Intention is to hodl Bitcoin for a long-term, i don't think there should be any cause for alarm, whether exchanges are leaving or not, exchange has never and will never be a good option for anyone to hodl Bitcoin for a long-term with, many comments has suggested non custodian wallet as a good option for that purpsoe, it means I will not be repeating that again.

Unless you are new to Bitcoin that is when you will ask if investor are to abandon exchange entirely, if it for hodling your Bitcoin,it is not adviceable to use them, but for p2p yes, but you must look for some how reliable ones, I said reliable because exchanges are not to be completely trusted.

If you have been following up with the history of centralized exchange on this crypto space, you would understand that there are some exchanges that have failed in the past, and that caused some investors to lose their money because they stored their coins on the exchange. Bitcoin is not to be stored on a centralized exchange, but for your own good, it is to be stored in a self custodial wallet.

If you don't store your coins on an exchange, whether it shuts down or not, you won't be affected in any way. There are many exchanges out there.

A reputable exchange can fail if it encounters some challenges that affect it so badly. It's only a scam exchanges that disappear without warning, but storing your coins on an exchange has never been considered the best option in the Bitcoin community.

We have been advised here time and time again by some experienced members, telling us never to store or hold our Bitcoin on centralized exchanges or other centralized platforms. If you want security, it's best you start using a self custodial wallet, like BlueWallet, which is compatible with mobile phones, and Electrum wallet, which is compatible with Windows.

Like many must have said already, not your key, they are never your coins. Don't let the fact that exchanges seems to make storing your keys simple and eliminate the idea of losing your keys to deceive you. There's no other safe heaven than storing your keys and leaving your funds in a custodial wallet. People who still leave their funds in exchanges are simply ignorant and have not yet been victims of exchange hacks or shut down where they will be deprived of their funds. Exchanges are not wallets, they are ment for trading your coins. They can't be trusted with your money and it's very much risky. Over the years we have seen different news of exchange been hacked and only a few of those money were recovered. Some users never got refunded..