I've been ex-directory, no calls offered, for over 50 years and never found a problem. How many people actually look up the number of a private individual in a directory? Do directories still exist - we don't have any?
I've not needed to do that! Businesses, yes, their numbers are on line, but as most people seem to use mobile phones for which there are no directories, they seem a pointless tool to find private numbers.
I've been ex-directory with BT for decades, but recently found out that the on-line directories are different. They had my name, address and telephone number listed. Apparently they get your details from several sources, such as Electoral Roll and Companies House. I had to email several of them to ask for my details to be deleted. Just today found another on-line directory I'm listed on that I didn't even know existed.
Yes, I'm listed on Companies House, OSCR and various statutory registers. But I don't think you will get my telephone number very easily nor my date of birth. Even so I do occasionally get one of "those" phone calls which I can answer with impunity knowing they don't know my number or who I am.
I have always opted out of the Open Register.
The on-line directories claim to gather information from a number of sources. I don't know for sure that they all had my telephone number but some claim to have it (you have to pay a fee to gain "credits" before you can see all the information they hold about you).
I found out about the on-line directories when a company phoned me. When I asked how they got my number they told me they used an on-line directory.