The justification of shareholders being the only ones who take decisions in companies is that they are supposed to have contributed most to its existence by providing the necessary capital.
However, this only holds true for those who purchased the shares from the company upon its capital increase (on the "primary market"). All the others never brought any capital to the company itself: they just bought their shares from a previous owner, on a second-hand market (the "secondary market" on the Stock Exchange). Their only role was to provide liquidity to this previous owner.
Therefore, the larger the number of financial transactions, the greater the distance between the current owner of the share and the investor that brought capital to the company, and the lesser the legitimacy for the shareholder to take decisions in the company management.
One way to translate this into reality would be that the Financial Transaction Tax be levied not only in money, but also in voting rights: at each transaction where the ownership of the share changes, a fraction of its voting rights (e.g. 1‰) is taken away, and brought to a pool managed by all other stakeholders in the company: the workers, the customers, representatives of the environment… all those potentially impacted by the externalities of the company.