Do you mean first to book in advance? Then people could squat on tickets, taking more than they need.
Do you mean first to arrive at the station? Then that's a drag on the economy as workers waste time being at the station early so they can get a seat on a train.
For city trams, subways and buses, it is simply first come (to the stop) first served. The solution is to expand capacity, as the economy is helped when large amounts of people are moved efficiently across the city.
Which is exactly what successfully managed cities do. There's usually something like a master plan that outlines the greater strategy for the next 20 years, or so.
Of course there's no expectation that it will be exactly implemented as planned, but is immensely helpful as a general outline and to define the overall strategy of where a city is going with things like housing, population, public and non-public transit, etc.
Or will you ration by saying that one person can only book one train a day?
For long distance train journeys, you
could have named tickets in that scenario.
All-reservation trains exacerbate the problems of "My first train was late, so I missed my connection" and "The train I booked was cancelled"Unless you can eliminate late and cancelled trains, which would of course be great.
The European train companies I know of are responsible for fulfilling combined ticket trips that are purchased as a single journey. If the first train is late, either the next one waits or they'll have to provide another transportation.
I've had a taxi ride home on the train company's expense when train was late and the last connecting train left already.
Your itinerary is 0930-1000 from A to B, and 1030-1230 from B to D via C.
You have a reserved seat on the 0930 and 1030, but the 0930 runs 40 minutes late and gets in at 10:40.
So you try to get the 1130. Except there's no seats available from B to D because someone has reserved the seats between C and D. The train pulls out empty from B, and you have to wait for the next train with seat available (1630)
Meanwhile the train gets to C, and people haven't turned up for their journey (reservations are free). Half empty train runs from C to D.
Reservation only trains are a terrible idea.
Imagine the chaos if the journey was free too. I'm going to London tomorrow, I'd book 5 different trains depending on what time I get up.
Either you come earlier and wait, or you pay more to secure a seat (and thus work longer to earn the cost but at least you won't compete with the poor), or the town/state pays for more capacity (and you work longer to pay more taxes to order and operate the new capacity).
Or you work longer to pay taxes to build more roads so that you can drive a "private" car instead of this complicated, pooled-cost public transport -- the point is that even a passenger car is anything but private when it comes to maintaining the infrastructure. Or you could only use private, toll-roads in which case you again work longer to pay for the toll.
It's always a drag.
Works fine for sub-30 minute rides (and a seat usually frees up at one point during your journey).
For longer journeys reservations are either part of the ticket, or available seperately if a guaranteed seat is important to you.
In my city, that won't work during rush hour because there's simply no space. The busses are filled to capacity, all seats taken and people standing toe to toe where possible. If you want to avoid intimate contact with strangers, you'll have to sit out a a few; if you don't mind it, you might still have to because there's simply no room.
Charging more so poor people have to choose sub-optimal routes also forces them to wake up way earlier in the morning because their "cheaper" routes take longer to get to their destinations.
First come first served works and, if people are getting anxious because there might not room in the bus/train, increase the frequency. If the costs keep going up then we might want to stop subsidising private companies by transporting their employees to the place of employment for free, i.e. tax them to cover the costs of public transport.
And how do you plan on doing that, once all the paths are taken?
There'll be a thousand challenges before "all paths are taken".
Only if they're losing productive time, i.e. working less. And in any case, most people don't want to maximise total productivity for the sake of it.
Plus, FCFS doesn't actually have to imply waiting in line.