What is the real benefit of AWS IAM permission boundaries?

That is not not purpose of IAM Permission Boundaries, nor is it the way it operates.

From Permissions boundaries for IAM entities - AWS Identity and Access Management:

AWS supports permissions boundaries for IAM entities (users or roles). A permissions boundary is an advanced feature for using a managed policy to set the maximum permissions that an identity-based policy can grant to an IAM entity. An entity's permissions boundary allows it to perform only the actions that are allowed by both its identity-based policies and its permissions boundaries.

To explain via an example, let's say that a developer needs permission to create an IAM Role in their software development duties. This can be a very dangerous permission to assign because they could create a Role that has full Admin permissions, thereby granting themselves even more permission that desired.

To limit their abilities, a permission boundary could be added to the developer such that they are only able to create an IAM Role if the role they define is attached to a permission boundary that limits the permissions of the Role (eg so it can only be used to access S3 and DynamoDB, but not other services). It can be a little confusing, but think of it as a set of rules that must be attached to any permissions they give, so that they can't grant full permissions. It's a way to grant them permissions, but limits what permissions they can on-grant to other entities.

This concept is totally separate to assigning IAM managed policies that you mention in your question. In most circumstances, assigning an IAM managed policy is perfectly sufficient. Permissions boundaries only really apply when somebody has permission to create new IAM entities.