Consider a scenario where I have £100 and decide to start a business as a self-employed individual. I invest £100 in inventory, but only manage to sell it for £100, resulting in zero profit. Under your hypothetical tax system, the tax authority would demand (let's say) 20% of my revenue, which amounts to £20. However, I don't have £20 to pay since I made no profit. Consequently, I am now £20 in debt to the state and essentially penalized for trying.
For a self-employed person, or a company, profit is analogous to an employed person's salary. Both represent the net flow of money or disposable income resulting from business activities or employment. This is why self-employed individuals and companies are taxed based on their profit, while employed persons are taxed on their salary.
Moreover, your use of the term "subsidy" is incorrect. A subsidy implies that the government provides financial support. In the case of a loss, the government does not send money to the individual or company. Instead, they simply refrain from taxing them, which is not a subsidy.
Note also in this example that in investing my £100, I likely generated tax revenue for the government through taxes on sales, salary, and profits on those who I bought from. So even though I paid no income tax, my activity still resulted in positive tax flows.
Then you wait for your updated tax return later in the year, which would automatically combine self-employed earnings, wages, investments, debts, tax deductions due to paying for childcare, etc... I normally have to spend 10-15 minutes to correct that if something like a travel calculation for my employer is wrong.