I understand why one would do solomining with a bitaxe, If a Bitaxe costs about $150, and you can make about 2-3 cents of bitcoin per day. Than it would take about 14 years without difficulty change to make your money back (i.e. will never pay for itself). Vs.. lottery ticket + more decentralization + big pay day + fun. 

Am I wrong? 

 I don't think anyone buys a bitaxe and hopes to make their money back. To most I'd bet it's a $150 hobby device. 

 It's educational. And better odds than the Powerball. 

 No