That's not true

You can take it at the same time and usually you take it in 2 hour intervals alternating.

You are not supposed to swallow them together or right after the other, that's right. But you can alternate them safely and take ibuprofen before the paracetamol starts wearing off (roughly four hours after the other).

Of course it's not ideal to take ibuprofen regularly for days on end. And don't exceed the maximum dose at any given time.

Personally paracetamol does nothing for me, so I rely on ibuprofen solely.

They are entirely different drugs with different mechanisms. Taking too much paracetamol/Tylenol/acetaminophen is extremely dangerous for your liver and dosing instructions should be followed exactly. Prolonged use of ibuprofen or other NSAIDs can lead to gastrointestinal ulcers and kidney damage, so only take it for as long as you have to. They both have instructions to take a dose every 6 to 8 hours, so if you're in significant pain or you have a really bad fever, you can alternate them every 4 hours. For example, paracetamol at 8am, ibuprofen at noon, paracetamol at 4pm, etc.

Also, be careful of "cough" or "cold" medicines like NyQuil/DayQuil, because they usually have paracetamol/Tylenol in them and that counts towards the daily dose limit.