I think it all depends on the individual. And over the last many years I have experimented with all the permutations.
1) In my own experience, I found that trying to drive while talking on a cell phone (i.e. holding the handset up to your ear) is
disastrous. Someone here who commented that it's not about losing the use of one arm, but about distraction of the mind, I thoroughly disagree. Don't talk on the phone, but try driving a car with only one arm. It's not good driving. To have to move your hand from the steering wheel to the gear shift is extremely extremely poor driving.
2) Talking on the loudspeaker was IMHO a little better, but still at least in my own personal experience I found I drive much better than the above, but I would not call it good driving. Especially if you don't have a mount for the phone, and are balancing it on the dashboard, or holding it in your hand while grabbing the steering wheel, or even placing it in your lap.
3) Talking on a bluetooth headset was smooth. I found my driving was 99% of what it is without talking on the phone at all. And that IMHO is acceptable.
But this is not to say that all people deal with it well. I suppose I would say I am responsible enough to pay more attention to the road than the call. So often I wouldfind myself not giving 100% attention to the phone call in a situation that required me to be focused on the road (such as when navigating through a narrow lane). I would even tell people to hold for 5 seconds in case I really need my full attention towards driving (ironically this would mostly happen when someone around me would be driving like an idiot, and lo and behold I would find them chatting on their phone while holding up the handset to their ear).
So would a bluetooth headset make a bad driver turn into a good driver? Certainly not. But would it turn a good driver into a bad driver? Not in my opinion. But talking on the handset directly or on the loudspeaker IMHO does turn good drivers into bad drivers.
My conclusion therefore is that it would actually be for the general safety of all to allow use of bluetooth headsets as opposed to talking directly or using your phone's built-in loudspeaker. And of course no amount of legislation and enforcement is going to replace our own individual sense of responsibility and duty. It is for each individual to decide if using bluetooth headsets also affects their driving adversely, and to be responsible enough to choose to not use them.
Of course not talking on phones at all is the safest. However, much like how telling people not to have sex doesn't prevent the spread of AIDs (the U.S. for instance has miserably failed on their abstinence only policies), telling people not to talk is not going to work. What you have to give people is the capability to take necessary precautions and prevention measures. In the case of AIDs, it is promoting the use of condoms, in the case of vehicular telephony, IMHO it is promoting the use of bluetooth headsets.