Yes that is one of the known issues. The legs would be wired thru contactors not just connected together. That way there can be a safe start up by push button or voltage sensor, and automatic current-sensing shut down if a plug comes out.Also, after thinking about this some more - the plug 'prongs' on the secondary and tertiary legs would be live the instant power was applied to the first one. Seeing as these are uncovered and extend from the plug it is lethally dangerous.
There is quite a bit of work to getting this right, including possibly a cross-phase lockout as per your previous post.
I'm envisaging a thorough design process here, with the wiring diagram properly reviewed up front.