So would a 50 log dive book with just OW cert or a 9 dive AOW cert dive book be better?
How bad, if uncorrected, can a diver become over 50 dives?
Not all experience is 'good' experience. 50 dives is plenty of time for complacency and sloppy habits to set in...for core skills to be forgotten and neglected...along with the creation of a false sense of capability.
If nothing 'happens' to go wrong on those 50 dives, it's far to easy to fall prey to the delusion of superior competence.
Without the development of skills and knowledge, along with some element of third-party assessment/testing to balance that, someone can easily become a pretty under-whelming quality of diver. Just saying...
A log book, even if genuine, shows nothing more that the dives you've done. It does not show what you've learned or how you've improved as a diver.
Is it an insurance thing or just because you have AOW cert you have the skills needed for that dive?
Liability can be an issue, but there are other factors.
Believe it or not, most dive operators would prefer not to have a customer death ever... so they do concern themselves over your safety. That means the application of prudent unilateral limitations - in the knowledge that there'll always be some divers who over-estimate their own ability and/or fail to set realistic and prudent personal limits for themselves.
What I would advise is that you do some honest self-reflection about your capabilities. What are your strengths and weaknesses? What elements do you need to remediate and/or refine? Consider the dives you want to do and research what skills, knowledge, protocols and competencies you
need in order to conduct those dives safely. Then pursue the training that helps you accomplish those goals...
AOW is a good means to accomplish many goals - if you concentrate on finding someone who will supply the training to your specific needs and requirements, rather than a dull 'off-the-shelf' package that only consists of dumb repetition of the minimum requirements...