Not really -- your argument sounds attractive, but is not always the best. People always have these grand fantasies about reaching doctors on call, but added redundancy does not always help. If something works 99.9% of the time, it is probably "good enough" for the expense, given redundancy already exists.
If docs were issued a prepaid phone for home call (would have to be an entirely different network e.g. Verizon(CDMA) vs AT&T's GSM), most likely somebody would forget to charge it (rarely used: I would estimate once every couple years) or forget to add minutes (most of them have expiring minutes over time), or the physicians would not want to carry it (another thing to carry / charge / drop / break / lose / clip to the belt with four other things.) The numbers would get mixed up -- would you rather have one number for the busy nurse to call at every nursing station / call operator, or 4 in decreasing order? Everything has to be grounded in practicality. A good paging network as cellphone backup is better.
A typical physician setup is email/blackberry for nonurgent, long communications (e.g. patients to see tomorrow AM when you get to the hospital.) For urgent communications most docs rely on a cellphone, and also carry a pager for the reliability (far above 99%) and increased range (much better than cellphone.) Landlines, as some of the people insinuated, are of course only practical when sitting at home or in an office.
Thus, my blackberry went out, cellphone went to VM, and the pager came through for me. An additional cellphone might have helped, but possibly not. If my pager happened to be out also, they would have overhead paged me throughout all hospitals I cover, which I would have heard and called back (this is how they did it in the old days anyway, and I was in a hospital at the time.) If I didn't hear this, they would have called my home, but I wasn't home anyway.
If all this failed, they would have called a colleague of mine. If he just got in a car crash, they would have called an in-house ICU doctor cover. If the in house intensive care doc just fell down the stairs and was out of commission, they would have called an on-call emergency doctor. If he was just kidnapped by terrorists, you're just being silly.
Point is, there's a lot of redundancy designed to make things safe already. There is generally decent technological support behind the basics. Electronic health records, that's another matter, and don't get me started... :p