Yep, even in the US, for a long while I kept a transactions register with my cheque book, and handwrote all my incoming and outgoing, like your dad.
That's why, when the US made pretty much all regular store transactions "immediate" it made things very convenient.
I don't know enough about the technical side of the way banks operate, but all I know is there was a point in the last few years when in the US it was announced that even a written cheque handed to a cashier, let alone a debit card, would be shown as deducted from your account balance instantly via electronic reporting. It meant that you couldn't wing it anymore....which was scary at first. But it also meant that your very newest balance would be constantly would be updated transaction by transaction, in effect anyway.
As that became the norm, for me it was a joy to be able to give up writing in my little register, instead knowing I can just access the info by phone or online. I still kept a rough overall tally mentally, but I just remember how I felt very freed when technology really made everything very instant and accessible, and I started to give up both chequebooks and their registers in which to write the transactions.