I wouldn't say Bitcoin has "solved" botnets but Bitcoin is botnet resistant due to its massive hasing power.  Average CPU has say 10MH/s on Bitcoin algorithm (probably less than that when you consider some botnet nodes are entry level and older systems).  Thus 8TH/s is at least 800,000 CPU.  The low performance of the average botnet node (due to specialized hardware like high end GPU) and massive size of Bitcoin network makes a botnet attack improbable but I wouldn't go as far as to say Bitcoin "solved it".

GPU-hostile blockchains make the playing field between average "good node" and average "bad node" much closer.  Achieving parity with an enemy that outnumbers you is likely a bad decision.   Simply put it is far easier for bad guys to amass large amounts of CPU power for "cheap".  Not just botnets, but rogue system admins, EC2 instances, etc.