I have avoided purchasing a trailer for the following reasons:
1. The hassle of transportation. It is bad enough that I have to break down my bicycle to put it into boxes to fly to various parts of the world to tour ... that is often quite a hassle in itself. But if I had a trailer I would have twice as much hassle. This goes for if you need to transport yourself and all your gear by airplane, bus, train, or even car rental.
2. The hassle of accommodation. If you camp, it probably wouldn't be too bad, but the moment you stay in a hostel or motel, you've got to do something with BOTH the bicycle and the trailer. Most of those places will reluctantly let you keep your bicycle in your room or will provide a little corner somewhere to store your bicycle ... just think how much more reluctant they would be if you indicated you wanted to store your trailer as well.
3. The expense. First, trailers cost more than panniers. Second, if you are trying to transport them all over the world with your bicycle, you would probably end up paying twice as much as you would for just your bicycle.
4. The weight. Nature abhors a vacuum. If I bring small panniers, I will fill them. If I bring large panniers, I will fill them. If I bring a trailer, I will fill it to overflowing. That's just the way it works. I have enough trouble climbing hills with my medium-sized panniers filled to capacity, without trying it with a trailer filled with three times that much stuff.
5. That moving parts thing Bikepacker67 mentioned. I worry enough about the odd noises I hear my bicycle make without worrying about the odd noises my trailer is making too. Also, there is at least one more tire to consider too (or do they have more than one wheel?). It will wear out along the way, and probably flat several times, and so you'll have to carry tubes and a folder for it, as well as for your bicycle wheels.
6. I rode a bicycle with a trailer, and although I know I would probably get used to the handling, I was all over the road with it.
If you are still considering a trailer, see if you can borrow one from a friend for a weekend and take it for a test spin ... see if you still like it then.