tmux's set-clipboard option controls whether a copy inside tmux is forwarded to the outer terminal using the OSC 52 escape sequence. When it works, copying in copy mode lands in the system clipboard even across an SSH connection, with no helper program at all.
The usual reason it does not work is the outer terminal. Many emulators disable OSC 52 writes by default because a remote host could otherwise overwrite the clipboard silently. In iTerm2 it is a preference under general settings, in xterm it requires allowWindowOps or the narrower allowC1PrintableSetting, and some terminals never support it. tmux also needs the capability advertised, which is what 'set -as terminal-features ",TERM:clipboard"' does on tmux 3.2 and later.
The reliable alternative is to pipe explicitly: bind copy-mode-vi y to 'send-keys -X copy-pipe-and-cancel pbcopy' on macOS, or wl-copy or xclip on Linux. Piping to pbcopy has worked natively since tmux 2.6; the old reattach-to-user-namespace wrapper is no longer needed on supported macOS releases.