Earlier quoted context omitted.
Except you don't need that because you can just return all four IP addresses for one record, e.g. api.x.com
I think if such a DNS/ip based round robin server is down, or replies 500 error, the client won't try another server Unless there's a way to get all ip addrs in js? By custom client code that queries the DNS system?
DNS resolution is handled by the DNS server and the browser. JS isn't involved, it's just telling the browser to connect to a certain hostname and the browser itself decides which IP to map it to (based on its DNS cache).
If the DNS server is down the website wouldn't load at all, but this is an acceptable trade-off considering DNS is a very simple system (not many things can go wrong) and servers can be redundant.