The airport probably assumes people can handle one carry-on bag and one personal item each without a trolley. There is often limited space for the immigration queues at busy times, and trolleys significantly increase the queue space per person.

The airports I've arrived at do provide trolleys at international baggage claim, where people will be collecting bigger, heavier bags, and often more than one per person, in addition to their carry-on and personal item.

Between areas of the airport

Some airports allow trolleys through passport control, check the text in this picture: https://commons.wikimedia.org/wiki/File:Copenhagen_Kastrup2.JPG This is between Schengen and non-Schengen part of Copenhagen airport.

In the other direction you can't see anything that will stop your trolley and you also see a passenger queuing with a trolley: https://commons.wikimedia.org/wiki/File:File-Copenhagen_Kastrup2.JPG

When exiting the airport

At some airports immigration control happens just before baggage reclaim. Bringing the trolley through to baggage reclaim would mean that it must have to go through a security check to get back airside. This would be too costly.

Another option is that you leave the trolley when you are in the front of the immigration queue resulting in a lot of trolleys ending up in an unwanted place so staff would constantly need to clear the area from trolleys, which would also be too costly.

A third option would be to have an airside area after immigration where you leave your trolley. Then there would need to be one way gates into baggage reclaim. Again too costly.

To slow you down.

Most of the routes and facilities between the gate and collecting your checked baggage is designed to slow you down, so the wait at the various points is minimised as much as possible.

By lengthening the routes and making people carry their own baggage, it spreads out the congestion at immigration etc, making it easier for the pre-immigration observations to happen and the backlog through immigration to be as small as possible.

There is a lot of thought that goes into passenger flow through airports at various points, and the airports goals are not necessarily the same as your goals. People tend to perceive inconveniences in different ways - the queue at immigration is often disconnected in people’s minds from the time it took to get there, so forcing people to spread out and arrive gradually rather than bunching up and arriving all at once tends to manipulate people’s feelings because they think the immigration line is shorter...