I see no problem with using remotely hosted resources for prototyping. But you should never let a link to remotely hosted fonts or scripts make it into production code.
Edit: Typo
That's certainly true of the server on which your APIs, if any, reside, but isn't it typical for your website itself to also leverage the CDN for distribution?
Basically, you should never have a production website which calls out to cdnjs.cloudflare.com or ajax.googleapis.com or fonts.googleapis.com, you should be hosting all of your site's dependencies in the same place or set of places.
As a side perk, your site also will stop looking like trash for users who use browser extensions to block such external calls. ;)
You are only as good as your local server. Having a cdn means you need a better local server.
I use webpack and other more secure/performant strategies for all my JS needs when working in a serious environment.
But when I am building something personal/light, I still load up cdnjs.com and drop something in. It's just easier than thinking about how I will serve files etc