Why the boundary decides speed, privacy and trust
Moving a task across the line changes more than where it runs.
Speed first. Work done before sending costs the site time and capacity, and the visitor waits for it. Work done after arriving costs the visitor's device time, and it happens after something has already appeared on screen. Neither is automatically faster. A page assembled at the source can arrive complete and usable in one go. A page that arrives as instructions can appear quickly and then fill itself in. The wrong choice is felt immediately: a blank rectangle that takes a moment to become useful, or a long pause before anything appears at all.
Privacy next. Information used before sending can stay where it is. Information needed after arriving must be sent, and once sent it has left. A site that decides at the source which records you may see can send only those. A site that sends everything and hides the rest has not hidden anything at all, it has merely made it less obvious. This is one of the clearest cases where the boundary is not a preference but a requirement: if the visitor should not have something, it must not travel.
Trust last, and it is the one beginners underestimate. A decision made before sending was made in a place the site controls. A decision made after arriving was made somewhere the site does not control and cannot inspect. Both halves can be useful, but only one can be relied upon. Every serious rule about what may happen, who may see what, and what a thing costs belongs on the controlled side, whatever else is also done for convenience elsewhere.