The problem I have is that it simply doesn't work.Hey!!
You'll will not able to use Truecallers dialer nor be able to see your contacts in our "contact tab" if contact access is disabled as you pointed out
You can still block calls in Truecaller by adding numbers to "My block list" in "More" tab. You will not be notified at all if they're blocked but that's not the case with the spammers provided in the CallKit list as you noticed (Call blocking & identification section) and they will still be able to leave a voicemail w/o contact access. To answer your question of why those calls aren't blocked is because there is no way to know if a call is blocked later which increases the risk of missing some important calls.
The CallKit list is basically an extension list of the spammers created when you allow contact access. It's called "SPAM" and is a contact which are the top spammers in your region (another reason for contact access). And those numbers are possible to block if you navigate to your phonebook > SPAM > Edit > Scroll to the bottom and choose "Block this caller". Again, you'll not be notified at all if they call you.
Please note that we use the contact information to generate a personalised graph which helps us to provide you with more accurate search results. Keep in mind that we never upload the contact information to our servers. That is against the Appstores guidelines. We only use the numbers to generate the graph.
Hope this clarifies a bit more. Don't hesitate to ask any further questions.
Have a nice day,
Kamran @ Truecaller
Since installing it (and allowing full permissions) I've had spam callers on a weekly basis and maybe 1/10 gets flagged.