Could this lead to a move by big investor to gain 5% of stock just so they can nominate alternative board members? Is this realistic? I understand almost no on

Could this lead to a move by big investor to gain 5% of stock just so they can nominate alternative board members? Is this realistic? I understand almost no one owns those kind of proportions today, but what would be the incentive today if everyone seeks diversification. This would create an incentive, would it not?