Generating a ±70 V supply for op-amp
Of course dual or split supplies are always nice, but George is right... its an expensive solution. On the other hand, your voltage divider is an often used solution for OP amp designs, if the signal is to be AC. To make it work as you described, you must add at least one capacitor, usually from the midpoint of the voltage divider to 0V, AND use a similar capacitor in series with the output to your load. Those capacitors can get pricy too, and bulky, as capacitor size generally increases with either capacitance or voltage rating. The lower the frequency you wanted to work with, the bigger that cap would get. 

Now my favorite approach to single supply OP-Amp circuits is to use a second OP-amp configured as a unity gain follower. This is similar to your first idea, except that your voltage divider midpoint would get connected to this second Op-Amp's (+) input. You'll still need a capacitor there for stability, but in this case the Op-Ajmp gain serves to amplify the effective capacitance. So, now that capacitor can probably be as little as 1/uF. Next, the output of this Op-Amp becomes the "ground" for everything else, including all ground points on your original (first) OP-Amp circuit, and it also becomes the ground for your load. This arrangement is usually called a "virtual ground", and you will have effectively created a split supply. Now your circuit will no longer need a second capacitor on the output and as a bonus, the frequency response of your output will now be good down to DC. (Of course if you WANT to limit low frequency response, you can still add a capacitor to the output.)