Earlier quoted context omitted.
I find what you have said harder to follow than just knowing debits are positive and credits are negative. The A=L+OE formula is a poor model for understanding accounting when the accounts dont fall neatly into those 5 high level categories. And unfortunately you almost immediately encounter accounts of that nature (accumulated depreciation and loans are great examples).
All accounts "fall neatly" into the broad categories, though. There are sub-categories for accounts with contrary normal balances for a given type of a given account category but they still summarize into their parent category. A contra-equity account (like "Owner draws") has a normal debit balance. That's contrary to the normal credit balance of an equity account. It still summarizes to equity and results in the own…
Harder accounts are things like tracking inventory. Yes you have the easy "Inventory" account on the balance sheet, but what about the "Opening Balance", "Purchases" and "Closing Balance" accounts that live on the profit and loss. They are all debit positive accounts but two of those always carry a credit balance and should be presented as a negative on the P&L.
If you want to be pedantic then probably those 3 accounts combined make up an expense account. But accountants split them out to make the financials easier to process. And the account split into 3 sub accounts for better presentation doesnt fit into the broad categories, but its still normal practice.