Whenever I see things like this, they are always tied to moving money from your checking to your savings account.
The reason why that's the mechanism they're suggesting is because most people treat their checking account as their primary transaction account - they leave their paycheck there, and spend out of it for daily purchases, bills, and so on. Perhaps also transferring a small portion to a savings account or other savings instrument. Most people tend to live on their debit card, or their credit cards (which they pay via their checking account), or on cash (which they withdraw from their checking account).
You seem to behave a little differently, which is okay, but to answer your direct question,
Is there any benefit to keeping money in a checking account?
The benefit is allowing yourself to separate a transactional account from a savings account. People generally like this separation because it allows them to explicitly separate money meant for longer-term savings from money they're intending to spend immediately.
In the US, the separation of a savings account from a transactional account is essentially regulated by Reg D which dictates that consumers are limited in the number of transactions they can make out of a so-called savings account. The purpose of this limit is to essentially force consumers to separate savings and transactional accounts. The fed wants this separation because it requires banks to reserve differently on savings and checking accounts, and if consumers ignore the different intended purposes for these products, it makes that reserve process much harder to implement.
If you've found something that works for you, then there's no need to change. Just make sure you understand if there are any limits on your savings account.