By not having an attorney, you will end up with less money, even though your lawyer will be paid from the settlement. This is because people without attorneys receive only 10% - 20% of the value of the claim (measured by the ultimate yardstick, namely the amount that a jury would award after a trial). In other words, the insurance company ends up keeping 80% - 90% of your money for itself.
With an attorney, however, you will receive more money because the insurance company has to pay 100% of the value of the claim -- not just 10% or 20% of it. This means that you will receive 67% of the value of the claim. The other 33% will go to your attorney, assuming his fee is that much. This 67% is obviously several times more than the "do-it-yourselfer's" 10% - 20%. (Remember also that with or without a lawyer, you also have to pay for costs.)
