My ds10 is an only and goes through this periodically. Yes, part of it is loneliness. However, part of it, I think is entirely normal to want (or think you want) something you don't have. Most families have more than one child in the US and many other countries around the world. Part of it is cultural, I believe. Many books, television programs, or other media forms revolve around siblings or sibling rivalry - and annoyingly so. If you're an only, you can feel left out of this cultural 'norm.' You can get the feeling that you'll never get to experience that sibling rivalry or sibling love per se. You're often led to believe that the perfect family is 2.4. Also, many products and other things in life are designed with two parents and two children in mind. So there are subtle constant reminders around of how an only is not the 'norm,' even though we, as adults, know there is no 'perfect' family or norm. It can be easy for only children to point to the supposed positives of having siblings and seeing only the negatives with being an only and not seeing the full picture.
I don't think parents of 2+ more children really understand the life for only children or their parents, imho. I just don't think they understand how decisions or choices are often out of our hands and not under our control with having children. Many people can be insensitive with it, I've found. Some only g/t children can be overly sensitive as a result because their relationship with their parents can be so close and intense. Also, many people will make comments about being them being an only child and sometimes it can be unsettling as well as being completely insensitive.
I, too, had my ds10 at a later age. Ds was born with some severe physical issues which totally consumed by time and energy. Needless to say, a #2 child never came and so we have an only. I do not regret for second with what's happened or having an only child. It's not what I originally planned or intended but I'm at peace with myself now. My ds is a 2e/pg and life has been rather challenging at times. I just can't fathom doing any of it again if a #2 ever came or we adopted.
On the bright side of life, the literature for an only g/t often speaks volumes though. An only child often receives more time, energy, and attention from their parents. And, oftentimes, the mother, in particular, isn't completely stressed out or sapped with an only child. That's something to bear in mind too.
And by the way, I'm the middle of three. Many times, I would have got rid of my older sister and younger brother in a heartbeat!
