Non-reserved seat limit on trains

Hello,
Just returned from Kyushu and wondered about this. I had a pass but person I was traveling with had to buy a ticket Nagasaki to Kumamoto. She wanted a non-reserved ticket to reduce cost but the agent said that was not possible. Do they limit non-reserved ticket sales? Or do some lines not allow non-reserved tickets? Thank you.

the Komame train from Nagasaki to Hakata is an EXPRESS train and is reserved seats only.

all SHINKANSEN trains that run on routes between Tokyo and Kagoshima have a certain number of cars designated as non-reserved and is determined by the train line and total number of cars.

while non-reserved cars have a limited number of seats, you are allowed to stand in the back, between cars and in the aisles if there are no seats available.

the train from Hakata, Tosu or Shin-Tosu (depending on what connection from Nagasaki they gave you) to Kumamoto is a shinkansen and you could have gotten a non-reserved seat on the portion of the trip.

Thank you for the reply. I suppose I'm wondering if there is an internal feature that allows personnel to know how many unreserved seats have been sold.
We just seemed to have issues in Kyushu with the rail pass as well. They couldn't validate the voucher in one place and told us to come back and then charged me for a seat as well. Perhaps they are just not that familiar with it.
We didn't have any of these issues last year in Tokyo or Kyoto so I'm just curious.
As well, got charge for a reserved seat from Yunohira to Beppu after the conductor told us to go to the non-reserved section. I will just print out rates from Hyperdia next time. Got too complacent.

The Kamome (not Komame) train between Nagasaki and Hakata certainly has reserved seats.

I don't know what exactly you asked the agent and what he told you, but at least one of you erred. It is always possible to buy non-reserved seat tickets.

Certainly has non-reserved seats, sorry.

By the way, non-reserved tickets are not bound to any particular train (they are valid on all trains on the given route for a certain period), so a system to track howmany unreserved seats were sold on a particular train is impossible even in theory.