I have been told repeatedly that I do not need to pre-book train tickets, but I am still wondering whether it would be worth it if we really want a certain train at a certain time(ie: the direct train from Leiden to Amsterdam, and at a specific time). We will always be travelling off peak. Would we ever find the trains full? Is it ever worth it to book ahead?
I do not believe domestic trains have seat reservations. Therefore, it makes no difference whether you buy 3 months in advance or 5 minutes before departure, it is still board the train and find a seat. Trains don't sell out. And they are so frequent that it is highly unlikely that off-peak there will be that many people on the train. This is mass transit. There is a direct train every 15 minutes to Amsterdam Centraal, and even more to Amsterdam Zuid.
You don't even need to buy tickets in the Netherlands. Just use your credit card to tap in and out at the gates.
If the train you want is crowded, you can just stand if there is room.
You can't make a reservation for a train. even buying a ticket for a specific train does not guarantee you a seat, nor would they deny you boarding. Even buying a ticket for a specific train, you are not bound to that train. I would just go to the train station when you are ready, tap in, tap out at Amsterdam Centraal, hop the soonest train going there, the ride is only 25 to 30 minutes. Like the subway in other cities. While crowded at times, I do not ever recall not finding a seat in a couple dozen trips on that route.
If you are really, really concerned, and cannot handle uncertainty, then purchase a first class ticket for a little more, hardly anyone ever sits in first class.
If you are planning to travel off peak, it may be worth purchasing your tickets through the NS app or website. You can get discounted rates which you won’t get tapping in and out: https://www.ns.nl/en/travel-information/off-peak-hours.html.
The only thing you need to do to be on a certain train is be at the platform on time.
Trains in the Netherlands are mass transit. They function like a nationwide metro system. Leiden - Amsterdam has a higher service level than many subway lines in the US... The Netherlands is about. the size of a major US metropolitan area.
So you just turn up, tap your CC at the gates, and board a train.
And if you buy a ticket it is good for on trip on any train on the route you bought.
That is actually how most trains work: You buy a ticket for a route, not for a train. And the ticket allows you to pick a departure at your own discretion. It is only for long distance trains with compulsory reservation that you better book in advance. But in the Netherlands that only applies to some services that leave the country.