The normal tablest in the US are 200mg: Lots of folks take 2 a few times a day: 400mg 3 times a day, as recommended on most of the packaging.
Prescription ibuprofen is 800mg tablets (most times). This is a fairly common dosage, 3-4 times a day.
600mg four times a day is inline with the BNF daily limit of 2.4g: http://www.evidence.nhs.uk/formulary/bnf/current/10-musculos...
Seriously the BNF is a brilliant resource, it has this to say about celecoxib: http://www.evidence.nhs.uk/formulary/bnf/current/10-musculos...
In acute cases paracetamol can have an 8 gram daily limit. long term you're going to see problems.
When you have something like arthritis, or and old joint injury, you'll be needing long term anti inflammatories
But I know a lot of folks will take ibuprofen for 7-10 days at those rates. It is pretty common, and just as common for people to regularly take naproxen a few times a day for chronic pain.
Taking pain killers regularly sounds absurd to you because you don't have that sort of chronic pain. And pain is a funny thing: My mother openly admitted that she would get to a point with migraines where the pain was so bad, the side effects didn't quite seem to matter (She learned to go to the hospital or doctor before then).
More often, however, these pain killers are the very things that makes every day life bearable. Some people it means they can be more active but others it just means they can open doors and grab toilet paper with less pain.
Your method is great for people that have occasional pain or needs: After all, it seems a bit silly to take it for no actual reason. And as far as the folks you know, well, if you are young that is more likely. And if not, it is just something the people you know don't talk about.