A world without borders has its pros and cons. I will relate it to my experience within Nigeria in the last three decades.
Within the country, the constitution guaranteed the freedom of movement from any part of the country to another. This has made many people travel from place to place for job, business, adventure and many other reasons.
A few years ago, when the problem of insecurity wasn't as scary as it is now, I used to travel around northern Nigeria where I have been living for the past sixteen years. The economy was also conducive for my movement then. Within ten years, I visited about 15 out of 19 states in northern Nigeria. I did most of the traveling with the sole aim of exploring a new environment, people, culture and learning in the process.
If there is no border in the world, I will replicate this at the international level.
I would love to explore all the seven continents of the world. At least, I will visit some selected countries in each continent, especially those countries with rich history and culture.
I see a world without borders making life easier for the populace in some instances. It would be easy for people to move from one place to another in search of knowledge and skills. From developing countries like Nigeria, there are many skills and educational training that the citizens can migrate to the developed world to acquire.
In a world without borders, importation of goods and even services would be much easier.
These two points have their disadvantages. If people are allowed to migrate without restrictions, some countries would become empty because all the citizens except probably the ruling class may leave in search of greener pastures. If that should happen, the developed places would become overcrowded and chaotic with time.
From my experience in traveling around Nigeria, I noticed this happening within the country. Many youths in villages are striving hard not to develop their birthplace but to travel to the more developed city and earn a living. This has contributed in no small measure to why the village remains the same, without development for decades. I once visited a local government where most of the ward councilors were residing at the state capital. The place that they were elected to represent was seen as too local for them to reside. If the world is without borders, something like this could happen at the international level.
Also, many people that travel to learn skills or get education would not return to their country to apply those knowledge to develop their land. If there is no restriction in importation because of the inexistence of borders, the unemployment rate would be more prominent than what we have presently in technologically less developed countries. The countries that can't compete favorably in the world of manufacturing would find themselves in a worse economic state.
Since the fear of insecurity isn't there, the problem of criminals infiltrating another land to foment troubles would not be obtainable. As a result of this, I will be visiting most entry points of foreigners in my country to meet people of diverse cultures coming to visit my country. I won't be afraid of relating with terrorists, gunrunners or other kinds of criminals.
My daily life would be about adventures. To be able to have the maximum opportunity to enjoy the voyages, I would engage myself in remote jobs and other online engagements. This will afford me the opportunity to work from Nigeria today, Canada tomorrow and from Australia the day after. What an amazing experience that would be.
On the possibility of such a world, I don't think it can ever be possible. Right from the beginning of the world, people protect their territories. Kingdoms fought one another in order to conquer others and expand their territories. There is no difference between the preferences of humans from that era and this era.
It will be difficult to have a world where there would be a direct movement without borders between countries.