If you follow the link to the "analysis" document it summarizes their rationale. It looks to me that the summary is "in reality we're not going to be sueing anybody, and we think the chances of a contributor sueing us are negligible, so while a CLA provides some extra legal protection/capability in theory, in practice we don't expect to use that and so all we get is the downside of extra bureaucracy and a barrier to contributors".

Different GPL projects vary in their attitude to the importance of enforcement -- the FSF cares a lot about retaining that option for their projects, but the Linux kernel community doesn't really care much. (And some kinds of enforcement, especially the most common "work with the violator to help them become compliant without taking legal action" kinds, work fine even if the copyright is not all held by a single entity.)

CLAs neither enable the kind of enforcement you mentioned, nor do they offer any additional legal protection mentioned in other comments. CLAs are good for exactly one thing, which is to provide an "out" regarding obligations that the license imposes. For example, if a project chooses GPL, a CLA can allow the benefitting org to disregard the share-alike clauses it contains, i.e., effectively allowing the org to use third-party contributions under non-reciprocal terms as if it were licensed to the project steward under, say, MIT- or BSD-like terms, or to relicense the project to a different, incompatible, non-GPL license in the future. Alternatively, a CLA for an Apache-licensed project allows the benefitting party to ignore Apache's termination clauses. These things create an asymmetric balance of power. Anyone operating under different beliefs can only be relying on a cargo-cult misunderstanding of what CLAs are actually about. There's no other reason to use a CLA.

My understanding (which could be wrong) is that it also allows them to change the licence down the road.

For example, if you've contributed code to an GPL2-licenced project, and several years later the maintainer wants to change the project's licence to BSD, having a CLA means that the maintainer doesn't need to ask contributor individually.

> I was under the impression that one of the (multiple) goals of a CLA was to empower an organization to actually go after license violations;

A copyright assignment would do that, but a CLA doesn't necessarily do that. You still can't enforce someone else's copyrights, only your own.

That was the reason for the FSF's assignment of ownership.