Why American homes are wired TNC-S and not TNC
We do use RCD (Residual Current Device) protection, and rather extensively these days even, it's just hiding in disguise

North American electrical wiring indeed started off as a TN-C (all protective earthing is accomplished by referencing things to the neutral) system, back in the bad old days before we had three-prong outlets and GFCIs (Ground Fault Circuit Interrupters), and evidence of this can be seen to this day (such as the abhorrently common NEMA 10).  However, two things happened:


Unlike Europe, who was coordinating a brand-new standard for wiring installs "all at once" if you will through the IEC process, protective grounding (TN-C-S) and GFCI (RCD) protection were added to the US NEC (the US wiring regulations, more or less) separately; furthermore, the GFCI protection rules in the NEC were phased in, location by location.
Our GFCI protection started off with wide adoption at the receptacle level due to the desire to retrofit shock protection into existing houses, especially in wet areas (bathrooms and kitchens).  This is in contrast to the IEC style of RCD, which was widely adopted in breaker form due to the larger number of new installs in Europe.


The consequence of these two things is that the sensitive UL 943 Class A GFCI, while widely deployed in the US nowadays, winds up performing a very different function to IEC RCD protection -- the former is designed to protect against electric shock, including "can't let go" hazards up to and including shock-drowning, while the latter protects primarily against fire, with protection against gross shocks as a side-effect.

Fast-forward a while, though, and the US, while having largely tamed its electrocution problem, still has a serious fire problem, partially electrical in nature.  This electrical fire issue is blamed on a variety of abuses and defects that cause what are described as "arcs", but are more precisely a surface-tracking type of fault where excessive current intermittently leaks through damaged insulation, slowly carbonizing/pyrolyzing it to the point where it smolders into an electrical fire.

As a result, electrical protection manufacturers in the US come up with what's called the Arc Fault Circuit Interrupter, or AFCI, that is designed to listen for the conducted-RF signature of these arc faults and break the circuit when one is detected.  Due to a combination of design limitations and accidents of history, though, the early AFCIs were built off of what basically is a GFCI platform, and as thus had a 30mA equipment protection ground fault trip function in them that is used to catch arcs-to-ground, despite the functionality not making it into the UL standards.

As a result of the rapid push to adopt AFCI breakers, and the retention of this GFPE trip functionality by 3 of the 4 North American breaker manufacturers (GE is the only one to have dropped it), in many cases, a modern house in the US will have RCD protection at the 30mA level on most branch circuits, with select circuits protected at 6mA.  However, this protection is provided at the level of individual branch circuits, not service-wide as is typically done in 5-continent power.  

Why is this, you might ask? Well, service-wide ground-fault protection is applied to large, low-voltage three phase services in North America to protect against fires, and works well in those applications.  However, the sensitivity of North American ground fault devices at residential-scale operating currents requires they use electronic ground fault sensing, as opposed to early IEC direct-acting RCDs that used the differential current in the measurement CTs to operate the trip coil without any sense electronics.  This has the upside that North American GFCIs were able to achieve reliable performance at low leakage levels early on; however, it has the downside that wiring a GFCI up backwards (with power being fed in on the LOAD side) will break it in a non-obvious fashion.

As a consequence of this, you can't reasonably use a GFCI as a main breaker in North America unless you are willing to take the same approach as the large wye services do, otherwise you run into issues as soon as you start doing other sophisticated and desirable things, like solar power.  Furthermore, the larger size of US services means that a central RCD would need to be excessively insensitive due to the simple fact the differential leakage currents are higher.