If by "debit history" and "credit history" you're thinking of how your bank transactions are recorded, then you may wish to look into the concept of accrual accounting.
Merely tracking cash in and out doesn't give you a full view of what the business is up to.
> accept that some figures won't reflect exactly the reality of the balance, since some compensations are done immediately (automatically) while others are performed, manually, days or week later.
Well good luck with selling your "eventually consistent" accounting system.
While I would prefer if accounting systems could be improved to record and aggregate uncertainty for those places where values entered are based on what is realistically an estimation rule (eg depreciation, stock valuation rules etc), the fact is that all such rules are stated as part of the reports. Within that framework, you report as correctly as possible to the cent or better.
Otherwise bad things happen. Accountants lose their charters. Executives go to jail. That sort of thing.
Serious business is ... serious business.