Tootsie's right - it's more about herd dynamics than trust. What is gained really depends on how you do it and why.
If done badly (that is chase horse in a pen until he gives in and follows you round) it does nothing much for the relationship except demonstrate to horse that you can outlast him and he might as well do what you want. No trust there - just submission.
If done well join-up can be achieved without having to round pen first - it is an acceptance of the handler as a worthy leader, and the establishing of a good relationship (and therefore mutual trust) and can take place over a period of weeks or months, not just five minutes in a round pen.
Round penning to join up isn't always appropriate or warranted either. I had a psycho mare who could never join up like that - to be driven away was always too much for her. Handling her without any restraint, and letting her decide how much we did worked wonders though.
Join-up is great for some horses, sometimes. For others it's confusing, or frightening, or just plain unneccessary.