The technical term you're looking for is "multiple unit", and you're correct that in a multiple unit it is not possible to arbitrarily couple together arbitrary carriages, re-arranging the multiple unit is possible only at dedicated maintenance facilities and may require a complete refit.

However everything else you've claimed is wrong. The designs you're talking about DO have motors under many (or in some cases all) passenger coaches driving the wheels, rather than a dedicated "locomotive" so they support your parent's point, not yours.

The original Eurostar (class 373) trains are confusing because they're built as multiple units but the lead and trailing cars basically just provide traction, so the result looks a lot like a "conventional" locomotive plus carriages. But modern Eurostar (class 374) looks exactly like any other multiple unit and has motors distributed across the whole train.

Britain does operate a bunch of locomotive pulled high speed (125mph) services, but it also owns a bunch of 125mph multiple units. Even the Desiro 444 and 450 trains could do 125mph if not for the fact they're configured exclusively for third rail power limited to 100mph.

The reason none of those trains exceeds 125mph is purely down to legal/ safety considerations. Britain uses coloured light signals with route control, as speeds increase drivers struggle to correctly interpret and act on a light signal by the side of the track. HS-1 (Eurostar) and many European high speed services have in-cab signals, so the driver doesn't need to try to observe fixed coloured light signals at the side of the track, the indications are inside the cab with them.

As well as the reasons given earlier about improved performance from distributing the traction power across the train, distributing the weight also improves crash performance. Heavy locomotives will tend to crush a lightweight passenger car, if we make all the cars of more similar weight this problem goes away.