That's precisely how they work. You install a client that pings their server. They see if there's an IP address change and switch the A DNS record.

If your DNS provider has an API, this is probably the very first example in the docs.

Why not? It is pretty simple and very fun! My first project in golang was a program that polled for the machine's IP address and updated a AWS Route53 record.

Its not exactly "write your own" I have a single line in my crontab that just uses curl to post to a url and the remote server takes the IP address it got the request from and sets the dns to that.

Though usually on firmware like openwrt the request going out is tied to a particular interface going up (and down) as it should be, so its somewhat more robust and 'correct' than crontab would be.