Thank you for the question! I love it!
First off, the brain is plastic which means it can learn and unlearn through creating new synapses and breaking down existing synapses. So although the gross size of the brain doesn’t appreciably increase, the brain is always changing. Cells in our bodies undergo senescence which is defined as gradual decline of functions. Neurons in our brains are not spared from senescence or aging. With age, the rate at which new synapses are formed slow down and the rate at which synapses are repaired also falls. Therefore, the aging of the brain inevitably leads to poorer learning ability and memory.
Okay, now to your question.
Even if the brain does not age, transplant would not be possible due to many reasons, one of which is immune responses. Immune response is a way our bodies are protected against pathogens like bacteria and viruses. All cells in organisms have a class of proteins/lipids known as antigens expressed on their cell membrane. Most antigens are specified to individuals and if they are in contact with immune cells of another person (basically what you will learn as white blood cells/ leukocytes), the immune cells will see the antigens as foreign objects and want to kill the cells. This will lead to full-blown immune response and death might follow.
However, saying that, we do perform surgeries of organ transplant such as heart and liver. Usually the physicians will perform immune compatibility checks and inject immune-suppressor to the recipient to prevent organ rejection. I don’t think much is known about the antigens on brain cells/neurons and so it would be extremely dangerous for a head transplant.
There are many other more factors that make head transplant extremely challenging. For instance, the technical difficulties of reconnecting blood vessels, not only within the central nervous system (CNS) but also between CNS and peripheral nervous system. Cell death is also something to worry about during head transplantation as neurons are very sensitive to environmental changes, and can die due to insufficient oxygenation during surgery. When these neurons die, the point of head transplant is lost as dead neurons also lose their synapses.
I hope I have given you a satisfactory reply.