Strictly speaking, the iPhone is not a necessity nor are cell phones in general.
I know what you meant by your question, though... and the reason I prefaced it thus is because, well, the answer too needs some perspective.
Can you function without the headset? Sure. The only advantage to a bluetooth headset over the included one is that it's not wired. That's all. It's not a question of whether you "must" have it, but whether or not wires are to you enough of a nuisance that it's worth the extra money to get a bluetooth headset.
If you have decided to get one, I will tell you from experience the Aliph Jawbone is simply the best headset on the market. Period. I've used more expensive Plantronics headsets and they blow. They're not as durable, they're not as clear, and they have no replacement part kits.
I broke the earloops on the Jawbone and sent for a $10 replacement earloop kit from the manufacturer. Other than that, the Jawbone itself is great... and it's one of the easiest and quickest to pair with iPhone or any other bluetooth-capable phone.
But it is $120 retail and the iPhone earphones are included and also allow you to hear iPod audio from the same unit. With bluetooth you have to switch to the wired headphone jack anyway to listen to music/watch movies.
Lately I've used the Jawbone less because I have an auxiliary audio input jack on my car and use the car's speakers in combination with the iPhone microphone as a handsfree without the encumbrance of having to put on or take off a headset. Plus I play all my music through there and it makes for a nice carphone that automatically silences my music when a call comes through.
Ultimately the decision of the value issue is yours... If you can justify spending $100+ for a headset, the Aliph Jawbone is the best one on the market, hands down.
Frankly, though, one should limit their usage of cellphones on the road... even with a headset, studies still show that this distraction does increase the risk of car accidents. Where I live that's a pretty big deal. I was recently in a very bad car accident on 635 in Dallas which is a very dangerous freeway. I do NOT get on my phone, handsfree or otherwise, unless I absolutely have to... because the slightest distraction on that freeway could get you killed. 25 percent of the drivers down here are uninsured.