A blog should live on a separate site from a law firm website. This enables the blog and the blogging lawyers to achieve a level of authority that cannot be achieved through marketing, which is what you have with a blog in a website.
Blogs separate from websites will be cited and shared more. Such a blog also opens up the door to guest posts from and interviews with prospective clients, strategic business partners and influencers who may shy from opportunities to participate in your website marketing.
Think of multiple blogs as well. Some individual lawyers have multiple blogs they publish to. Many law firms have multiple blogs. Each of the blogs is engaging a different audience. People follow a blog, not the law firm.
You cannot cover multiple topics on a blog anymore than a magazine could report on both fly fishing and modern brides.
The goal of your blog is not to draw traffic to your website, the goal is to grow relationships, and a word of mouth reputation as a “go to” lawyer or “go to” group in a niche. Focus on developing business and a career, not traffic to a website, which I hear as the argument for a blog in a website.