Crypto exchanges going down during times of high volume is definitely a thing, yes. For example:

https://www.coindesk.com/coinbase-redoing-infrastructure-to-...

> During the recent bitcoin bull run, Coinbase has struggled to keep itself up during stretches of heavy volume, leading to snarky comments on Twitter and Reddit that it’s only news when the exchange doesn’t go down during peak periods. Given the exchange has filed preliminary documents for a public listing of the company’s shares, fixing its infrastructure has undoubtedly taken on an even greater urgency.

Going down is one degree lower than officially displaying a 'you cannot buy <security>' on your app. I know DDoS smell bad but it's not the same. And mind you I lost profits on the latest DDoS.

Coinbase suspended XRP. Not a perfect comparison, but perhaps closer to what you're referring to.

It was due to the SEC, not unofficial influences.. I think it's a different topic

Don't forget that crypto exchanges have none of the properties of cryptocurrencies themselves, in terms of censorship resistance and cryptographic guarantees. Since fiat currencies are involved and these are businesses operating in countries with laws, they have to enforce whatever the government wants to require of them. They can absolutely halt trading, or freeze funds or assets on their platform at any time.

DEXes, however, can be designed so that no person can halt trading or freeze your funds (usually you trade out of your own wallet anyway). A DEX is just a computer program running on the Ethereum blockchain. Once deployed, the blockchain is immutable, and it just sits there accepting orders.