Wouldn't a dozen prepaid SIM cards mean 12 times as many things to defend? Also wouldn't anyone you paid to "do it for you" need to be trusted, undermining the no-trust principle of cryptocurrencies?
Yeah, it would require some thought. If you randomly rotated through the different sims it might help. I was thinking that someone else might be a good idea so that it would be harder for an attacker to figure out your number. I'm assuming that if you buy any phone service, prepaid or postpaid, that someone would be able to find it on those people search sites. But maybe all you really need is to have a number strictly dedicated to each value store, never used for communications.