sites like this are neat until you remember that curl's willingness to write ansi escape codes to stdout when it is a tty (as this site relies on to format the output when the user agent is curl) is actually a security vulnerability.
tldr: There are a variety of ways that attackers can cause you to execute execute arbitrary code when you echo their maliciously-crafted data to your terminal. Therefore, when you run curl without redirecting its output, or when you cat a file you've downloaded, you're trusting the server (and also the network, when you don't have https:// in the url) not to exploit you.
Of course the terminal emulators are ultimately to blame but when there are so many problems in so many of them, imo curl's default behavior should be to filter its output when writing to a tty.
You can redirect curl's output to a file with the -o filename option (or with > filename for shell redirection). But in the case of sites like this which output ansi-escape-formatted data that isn't very useful.
Also, after saving unknown data to a file it's common to look at it with less or perhaps xxd or strings or file ... all of which have had their own CVEs in recent years 🤦