Not grounding the isolating transformer's secondary side socket's PE pin is for safety. If you are using an isolating transformer for electronics bench repair work, odds are you are going to introduce a ground to some part of the DUT (device under test) by connecting the ground clip of your scope probe, fully knowing that doing so on the primary side of its PSU, or anywhere in a DUT with other high voltage circuits looses you the personal safety benefits of isolation.
As such, your bench environment should be carefully assessed for safety when working on a live DUT, one of the most critical issues being the risk of coming into contact with a live conductor and ground at the same time resulting in electric shock or electrocution. As long as you aren't in contact with ground, a single point of contact with most live circuits wont shock you.
(I exclude high voltage pulse, and high power RF circuits that can shook you through your body's capacities coupling to ground.) As many who didn't have repair trade training back in the '80s will be unfamiliar with a safe(ish)
# workspace for working on live DUTs I'll briefly detail it.
(I'm not licenced to *teach* the old TV and entertainment equipment repair course and it was a looooong time ago so I may have missed something)To minimize the risk of ground contact, the flooring should be non-conductive
*, the bench *MUST* *NOT* have a metal top, any metalwork under the bench surface or along its front you may come into contact with should be isolated from ground, and any grounded metal fixtures in the room within 2m of your work position should be insulated to prevent contact.
Test equipment should be divided into two categories, #1: designed for floating operation, and #2: inherently grounded (e.g. most scopes), and non-essential items in #2 placed somewhere you'd have to move away from the DUT to access. The remaining essential #2 items present a risk of personal grounding so should be in one specific area of your bench as far from the DUT as reasonably practicable, and you must obsessively develop the habit of *NEVER* reaching for them while your other hand is near the DUT. That means *NEVER* adjust the scope while probing with a hand held probe - either find something to clip the probe to or STOP, power down, and solder in a small loop of wire to clip the probe to.
Beware of grounds from unexpected sources e.g aerial cables or signal cables to monitors etc. Aerial cables should have dedicated isolated sockets, and if there is a preamp or LNB that requires power, a power injector should be used on the aerial side of the socket. Its rare to need to work on the primary side of a DUT while connected to a monitor, as its usually sufficient to simply check the secondary side voltages. If you do, the monitor should be dedicated (i.e. not shared with your presumably grounded bench PC or other grounded signal source) and designed for floating operation (i.e. either battery powered, or with a factory-fitted two pin mains connector).
While you are working on a live DUT, all colleagues, family members etc. *MUST* know and understand not to approach you, and should know how to safely isolate power to your bench in the event that you do receive a shock and require assistance. Also, young children and pets should *NOT* be permitted access to your bench area
* Concrete, quarry tile, and dirt floors, can be sufficiently conductive to ground you. If you have such a floor, use a thick rubber or plastic insulating mat extending as a minimum the full width of your bench, under it and 2m from its front edge. Sub-grade basements with permanently damp floors are unsuitable for use as an electronics workshop. Carpet can also be problematic as any spills may make it conductive, and you probably have no idea of the location of any grounded pipes, wiring and other metal objects under the floor. Again use a mat, but on carpet you can get away with simple flooring vinyl, as if you keep the carpet under the mat dry and reasonably clean it will also contribute insulation. It has the side benefit of making dropped small parts findable! 
# Such a workspace relies on the user avoiding ground contact, which requires training, continued concentration and no distractions. As such in the 2020s OSHA, HSE and other national safety bodies would probably classify it as an unsafe workspace! 
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