If you don't pay any tax and you claim the tax the company has...

If you don't pay any tax and you claim the tax the company has paid on your behalf -then effectively the company has paid no tax as you have been refunded same

The company makes a profit and is taxed on that profit
After tax the company pays out a dividend to its owners, the shareholders.
This dividend is treated income to the shareholders and is thus taxable and added to their income from other sources e.g. wages, interest, capital gains, rental receipts ect.

However as company owners they have already paid tax on this income they are granted a credit, franking, so as not to be taxed twice on this income. This is the purpose of Franking Credits to prevent double taxation on dividends from company's that have paid tax

If you're in a position whereby you don't pay any tax you cannot be taxed twice, you're not taxed at all. Therefore you lose the franking credit.

Were you to keep the franking credit then, upon the dividend you received, the government would effectively lose the tax paid by the company

Someone has to pay the tax.