It ultimately depends on the person using it.

Lather is often associated with a soap's cleansing qualities, which is usually desirable. But some people prefer their soap to be more moisturizing than cleansing.

I personally find pure castile soap to be too moisturizing and not cleansing enough. I prefer a more balanced soap with a bit of both qualities.

Does it actually make the soap more cleansing, or is it just a perception thing?

My understanding was that, when companies add lathering agents to their products, it's the same as dyes and fragrances: really just there for cosmetic purposes.

Surfactant types and levels are different from different ingredients. That's what does the "cleansing" you're asking about. Not all oils and fats clean the same way. Some are better for different "messes" than others. Like wood ash makes a fantastic soap to strip grease. However, it also dries the hell out of your skin and can lead to lots of cracking.

It's all a balancing act as to how strong of a soap you want compared to damaging.