So the apparently contradictory statements that "most trains have plenty of room" and "most passengers find the trains overcrowded" can both be true !
Exactly what we see and have learned. Calculations on your hypothetical example:
100 "heavily overcrowded" with seats for 700 but 1200 on board
900 "light loading" with seats for 700 but just 100 on board
1000 services
Total seats 700,000
Passengers on overcrowded journeys 120,000
Passengers on light loaded journeys 90,000
Total passengers 210,000
Total seated passengers 160,000
Total standing passegers 50,000
Passengers reporting "heavy overcrowding" - 57%
Trains heavily overcrowded - 10%
Load ratio on these trains - 171%
Passengers reporting "light loading" - 43%
Trains lightly loaded - 90%
Load ratio on these trains - 14%
Passengers standing when they travel - 24%
Seats occupied - 23%
What you see in the press:Passengers reporting "heavy overcrowding" - 57%
Passengers standing when they travel - 24%What you see when you work out the line's economics:Less than 1 seat in 4 occupied on average (23%)
9 trains out of 10 carrying just 10 people per carriage
Overall loading 30% It's very instructive to look at passenger numbers based on published ticket sales data, and to work out the number of seats based on timetables and stock used, and come up with an estimate of actual figures; easy enough to do for a branch line on which you can assume that most of the traffic runs to or from the junction station, much harder elsewhere.