The Piccadilly Line was opened in 1906 for gods sake, forgive them for not catering to people with 3 suitcases very well! That's part of the reason we built the Elizabeth Line, to enable a better transport option for people coming into heathrow.
Other way round is my understanding. Road based transport was for the poor, especially trams, and the underground was for the fancy folk looking to shortcut past all of that.
relative to their wealth
But total wealth was a lot lower than today, while clothes were much more expensive relative to the average income than today. Many people wore their best clothes on Sundays only, and street photos from the same period show that an average person was dressed rather simply.
I don't even think that the tube was affordable to average working class public. When I read historic accounts from much later (the 1930s), they mention that fare on public transport was expensive enough that you had to choose between a breakfast and a ride.
It is interesting how infrastructure silently reflects society of its time.
In 1906, people travelling with three suitcases would likely have servants carrying them, and no one cared particularly about comfort of servants.