You are missing a very important detail, which is that if they are tools of the capitalist class, it's the capitalists making decisions and the amount of "power" individual politicians within that apparatus have is essentially a mundane question of administrative structure. Putin the capitalist puppet is no more or less dangerous than a hypothetical quadrivium of capitalists puppets would if they collectively had his power.
You are missing a very important detail, which is that if they are tools of the capitalist class, it's the capitalists making decisions and the amount of "power" individual politicians within that apparatus have is essentially a mundane question of administrative structure. Putin the capitalist puppet is no more or less dangerous than a hypothetical quadrivium of capitalists puppets would if they collectively had his power.