I also have this same question, although im not on the free version of esxi, (im running a multi-host VCSA 6.5u3).
and using VMRC.exe on win10.
clearly VMRC.exe can remember user/pw, and by using a win shortcut like this below, i get to the same point as OP.
"C:\Program Files (x86)\VMware\VMware Remote Console\vmrc.exe" "vmrc://administrator@vc.xx.xx/?moid=vm-7763"
the credentials fields comes up fully populated, such that i just have to click connect and then im in the remote console session.

So like OP, im trying to find a way to automate (or bypass) the clicking of the connect button.
(im aware of using PS to script generation of ephemeral [VC-CLONE-SESSION-TICKET] tickets -> URL , as well as using autohotkey to script the <enter> or <mouse-click> part, but i wanted to confirm that there is not some native way to accomplish this, first).
in other words, why require a prompt for credentials input, if all fields are already, correctly populated.
(maybe a flag needs to be passed to vmrc.exe?)
thanks!