I'm not sure that there is a good answer to the manager's question. In some contexts, having formal gate reviews may be beneficial. However, reviews tend to be after-the-fact inspections, which aren't the best way to build quality into a product.
I'd recommend rethinking what you mean by "review". For example, the Three Amigos can help you during requirements engineering and planning activities to make sure you're getting all of the perspectives on a piece of work. Instead of having an after-the-fact review, all of the key people are collaboratively doing the work together. Similarly, using pair or mob programming to develop the software may reduce the need for any kind of formal code review.
Specifically, as a test manager, I wouldn't want to enforce reviews. Instead, I'd want the people who will be testing the system to be involved, as collaborators, from the beginning of the effort all the way through the end. I'd also want the other team members - developers, designers, project managers, product managers, business analysts, and so on - to be involved and invested from the start all the way through the end of the testing process to make sure that issues that do come up in later testing can be effectively triaged and resolved.