As already mentioned most new investors will want to see a version of your up-to-date cap table before investing. Beyond this, equity management software such as eShares (where I work) allows companies to give investors real-time access to their cap table (after they invest), so investors can check your cap table anytime without having to ping you or your lawyers. Over 80% of companies do this--whether sharing their full cap table or a summarized version.

Cap Tables aren't usually private. I don't recommend advertising it on your website but, certainly, any new investors will need/want to see it before committing.