The ease of deployment offered by almost universal roller furling
on headsails has led to an awful lot of people sailing under headsails only much of the time. If you're not racing or not a purist, for the most part it's fine as long as, as mentioned above, balance doesn't become an issue.
Where the "don't do it upwind" school of thought comes from, I believe, is an incident in the Caribbean where apparently 3 charter boats lost their rigs
in largish seas on the same day, all sailing headsails only. Sailormon's comment above:
"A properly supported, well-tuned mast is held erect and in column by it's supporting stays and shrouds, and, unless you're carrying way too much sail area for the windstrength, it shouldn't begin to overstress your rig."
is right on... the three boats in question were early versions of the late '90s backstayless rigs