Solo travel has to be one of the most freeing experiences. I took my first overseas trip alone back in 2010 and followed it up a couple more times. I had many similar experiences to you, such as alone but never lonely, freedom to do as you please.
Of course, I did have moments when being alone hurt a little, such as the first couple of hours in the first destination. Having spent nearly 24 hours travelling and just having that feeling why did I do this.
There was also getting lost. Back in 2010, I did not own a smartphone, there was no mobile Google Maps. I decided to try and remember where to go and end up walking in the opposite direction for 20 minutes.
Travel solo is such great advice for almost anyone I think.