This is good advice, not least because an avoidable single point of failure is never good.
I have my domains with a registrar, hosting elsewhere. Recently my former hosting company, FatCow, suffered a catastrophic router failure that took down everything - their home page, all customer sites, control panels, the lot. Infuriatingly, this happened right after I sent out an important marketing message. Because I wasn't registered with them I was able to move to a backup service as quickly as I could sign up for an account and change nameservers at the registrar. (Propagation took a while, but it was working for some people very quickly.)
I think you're technically increasing your points of failures by splitting domain and hosting.
You're not adding redundancies by splitting the services. Since these are mission critical services, if either fail, everything fails. Now by splitting up the services, you're increasing your risk of failure.
Take this scenario as an example. Suppose a random host will fail 1 out of every 500 days. Well now you have two hosts that could fail on 2 random days out of 500 days instead of just one host that'll fail once for every 500 days.
The above is not exact but i hope it gets the point across. I'm not saying dont split hosts, I do that myself. I'm just saying don't think you're limiting point of failure by dividing mission critical services apart. You need redundancy for that.
No: if your registrar goes offline for months you have not lost anything but your ability to update your DNS entries and renew your domain. Your registrar is NOT a mission critical service: it is the only way for you to recover if your DNS infrastructure needs to be replaced.
A dedicated DNS provider will provide a very good level of redundancy, for example DNSmadeeasy give you 5 nameservers to use which I believe are all hosted in different datacentres.
I have my domains with a registrar, hosting elsewhere. Recently my former hosting company, FatCow, suffered a catastrophic router failure that took down everything - their home page, all customer sites, control panels, the lot. Infuriatingly, this happened right after I sent out an important marketing message. Because I wasn't registered with them I was able to move to a backup service as quickly as I could sign up for an account and change nameservers at the registrar. (Propagation took a while, but it was working for some people very quickly.)