Why bother referencing neutral to ground in residential transformer?

I’m going to list the 3 scenarios for electrocution I can think up for both a residential transformer with grounded neutral and an isolated transformer. I find that the grounded neutral transformer has one more scenario in which I get electrocuted than the isolated transformer does and I want to know why despite this, we reference neutral to ground in residential systems. I have heard it is for safety reasons but my thinking suggests that it is actually more dangerous to reference neutral to ground. I’m hoping someone can clear this up for me.

Imagine I’m standing at my main breaker looking at my hot and neutral lugs. For all of the examples below please imagine I’m not standing on any insulated platform. I’m barefoot on some kind of wet concrete floor. I’m also explicitly talking about the service entrance wires to do away with any complications coming from different branch circuits inside the home. Please assume I’m just talking about the service entrance wires.

I’m also going to talk about the current as if it were DC current and electrons come from the hot lug towards neutral. This is just because it helps get my ideas across in English easier. But please understand that I do realize that current will be flowing in both directions on an AC circuit.

Regular Residential Transformer w/ Grounded Neutral

1. I touch the hot lug. There is a potential difference between the
   wet concrete floor and the hot lug. There is also an unlimited
   source of electrons (ground connection at neutral) connected to an
   unlimited acceptor of electrons (wet concrete floor). Current flows
   from the ground connection at the transformer, through my body, to
   the wet concrete floor and I get electrocuted.
2. I touch the
   neutral lug. There is no potential difference between the neutral
   lug and the wet concrete floor since the neutral lug is grounded and
   I do not get zapped.
3. I touch both the hot and neutral lugs at
   the same time. Current flows through my body (in addition to flowing through my body to the wet concrete floor) and I get electrocuted.

Isolated transformer (Neutral not grounded)

Now imagine that my residential transformer was not referenced to ground at the neutral point. Imagine it is like an isolated transformer.

• I touch the hot lug. There is a (very likely – but unknown) potential difference between the concrete floor and the hot lug. However, there is no unlimited source of electrons like a grounded neutral. There is a limited source of electrons which is the wires inside the transformer themselves. I may get a small shock similar to static electricity shock as my body and concrete floor get brought up to the same potential as the hot lug but ultimately there can be no flow of electrons because there is no sustainable source for them to come from. They will push into my body because of the potential difference but at some point the transformer conductors will be so electron deficient that the force on the electrons to stay will be greater than the force they feel to push into my body.

• I touch the neutral lug. It is unlikely that there is a potential difference between the neutral lug and the wet concrete floor so I will very likely feel no static-electricity like shock. In addition for the same reasons as above, even if there is a potential difference between the neutral lug and ground there is no sustainable source for electrons to come from so again I do not get electrocuted.

• I touch both the hot and neutral lugs at the same time. Current flows through my body and I get electrocuted.

Electrocution Breakdown

• Regular Residential Transformer w/ Grounded Neutral: Cases (1) and
  (3)
• Isolated transformer (Neutral not grounded): Case (3) only.

So given this breakdown why do we ground neutral? Seems like it only introduces scenarios to get electrocuted. We could even have ground faults with an isolated transformer and not get electrocuted. Seems more dangerous to ground than to not.