I can see how having QuickBooks Online Class Tracking available in Simple Start would empower your business to further categorize your transactions while still saving on your monthly subscription. I'm preparing a feedback report to send up to the Development Team for review. All it takes is a voice much like your own to bring the changes we all want to see in QuickBooks.
Regarding the Accounting Method, the option you select between Cash and Accrual in Account and Settings is only used in the Close the Books process within QuickBooks Online. For things like Reports, the setting will always be defaulted to Accrual unless you customize the report. Check out the instructions below to create a Cash Basis customized report:
Saving a report in Cash Basis
From QuickBooks Online, navigate to the Reports tab. Select any report you'd like to save in Cash Basis from here.
Under Accounting Method, select Cash Basis. Configure the rest of the report in a manner you'll be checking on a regular basis.
Select Save Customization and enter a name for the report, such as Cash - Profit and Loss.
We also offer a guide on changing your accounting method for your convenience. Please keep in touch with me here if there's anything else you need, I want to ensure your success. Thanks for bringing your question to the Community, hoping you have a wonderful holiday season.