First of all, if there were easy entry to the market it could not, by definition, be an oligopoly. If barriers to entry were to be lowered, profits in an oligopoly would disappear. The oligopoly would likely become a market in monopolistic competition and economic profits would drop to zero.
In an oligopoly, there are only a few firms because the barriers to entry are so high. This means that there is very little competition for market share. Therefore, prices can be kept high and economic profit can be made. But this situation disappears if the barriers to entry are removed. Now, any firm can enter the market.
When firms enter the market, the supply of the good or service being provided will go up as well. Simple supply and demand analysis shows us what happens when supply rises. When supply rises, all other things being equal, equilibrium quantities will rise and equilibrium prices will fall. As prices fall, the firms in the oligopoly can no longer make as much profit as they once did. If the barriers to entry fall, the market will be flooded with new firms and economic profits will fall to zero.