I don't think Putin has a single reason, the reason you stated is one in particalur an US one. From a Western European view, my best guess is, he also wants to destabilize EU (with a lot of NATO memebers). Remember Syria an the refugee crisis? This gave TailWind to a lot of right wing parties, which are mostly ProRussia (AFD, FPÖ etc). Incidentally left wing parties, "Die Linke" comes to mind, are also Putin fans. So any polarization within EU will help Russia to sell its resources and don't get sanctioned to much. IMO Putin is playing the divisor.