The author of Best practices for DNS forwarding [petri.com] recommends using the ISP's DNS servers as forwarders instead of doing the recursive lookups yourself, the main reason being performance. This makes sense as you're only doing one query, getting the response probably right away, given a big enough cache at the ISP and a popular enough website.
A downside of using your ISP's DNS servers might be their stability. It used to be the case that ISP's often had not-very stably DNS servers. However, this can be solved by simply forwarding to name servers such as 1.1.1.1, 8.8.8.8, or 9.9.9.9.
What are the benefits of doing the lookups yourself?
Edit: Using public name servers like Quad9 also adds in security as it filters out known malicious domains.
Benefits to resolving yourself include not being dependent on, or trusting, a third party to do so. This includes ISPs that may change, and public DNS that collect your data or impose their idea of filtering.
If a DNS service meets your needs, certainly forward to it.
To answer my own question...
John is correct in stating that "if a DNS service meets your needs, certainly forward to it." A few reasons why it may not meet your needs:
A reason for running your own resolvers:
If both options (own resolvers or public ones) both are valid options for your company, you can chose which to want, depending on personal or architectural preferences. Of course, running your own resolvers means more systems to manage, you need to have system administrators with DNS knowledge in your team, etc.