Advice for buying car without logbook

Hi friends.

I am back again and again for your advice.

We have found a car we love, ticks all the boxes mechanically and physically etc.

Only issue is that it is missing the logbook, Has one owner, a mum upgrading her car and she said the logbook was lost ages ago her kids pulled it out to read on a trip one day and then no clue where it went from there:

In saying that, she has continued to “logbook” service on time and kept all the receipts and detailed list of service actions in a binder as a replacement logbook of sorts. So the car shows a full service history, just no physicial book.

Would you guys consider this okay?