"echo" and "time" are explicitly bash built-ins, "which" and "cat" are not, and you will always get a process spawned there.

Your second strace is misleading, you didn't trace child processes.

    $ strace bash -c '$(which echo) hi' 2>&1 | grep 'exec'
    execve("/bin/bash", ["bash", "-c", "$(which echo) hi"], 0x7ffddfcdaee0 /* 59 vars */) = 0
    execve("/bin/echo", ["/bin/echo", "hi"], 0x55eb565cb0b0 /* 59 vars */) = 0
    
    $ strace -f bash -c '$(which echo) hi' 2>&1 | grep 'exec'
    execve("/bin/bash", ["bash", "-c", "$(which echo) hi"], 0x7ffd09b3e228 /* 59 vars */) = 0
    [pid 81493] execve("/usr/bin/which", ["which", "echo"], 0x5560d172e0b0 /* 59 vars */) = 0
    execve("/bin/echo", ["/bin/echo", "hi"], 0x5560d172e0b0 /* 59 vars */) = 0