Taxes don't affect competitiveness much. They only affect profitability, because any money they use to compete and any money they never earn because they compete by lowering prices isn't taxed anyway. They only pay taxes on profits. Taxes are not a business expense.
There is perhaps an indirect link to competitiveness in that a company can retain profits and use them down the road to take over other companies, which may strengthen their position in the market. Another such indirect link is that profitability affects the company's ability to raise capital.
But what I believe is that it's not so much the company itself that cannot afford to pay higher taxes, it's the management team. If a CEO doesn't optimize taxes for the benefit of owners/investors, that CEO could be replaced by someone who does.