I'm with you so far.
> the goal is to keep the accounting equation true at all times
Perfectly reasonable.
> For example, you sell a lemonade for $5. You add $5 to Sales (Income) and add $5 to Current Account (Assets).
And now you've completely lost me. Money appeared. Lemonade disappeared. I want to see the corresponding +$5 and -$5.
Making it fit the equation (Equity + Income + Liabilities = Assets + Expenses) is not an intellectually satisfying reason for 'Assets' to go up by $5 when I just lost $5 of assets.
What if it worked this way in physics?
I could write
Force * mass = acceleration
1N * 500g lemonade = 0.5 m/s/s
Then I could say: "If we halve the mass of lemonade, then we double the acceleration:" 1N * 1000g lemonade = 1.0 m/s/s
And then you could say "But you didn't halve the mass, you doubled it!" and then I could say "Yes I did, look, the equation still holds."