While I walked with a club (SUBW and Kamerukas) in my teens and twenties, I now do all my multi day walks solo. This may change a little when my partner joins me for an easy weekend or two over summer.
TO me the benefits are:
Able to plan and do the walks I want to do, when I want to do them, at a pace and in a style that maximises my enjoyment - no joint decision making. Example - I walked the Vosgues section of the GR5 with 2 friends. Their idea of the walk was to head as fast as possible to the day's destination and then lie around reading. It caused some angst if we did not reach the predetermined destination, or that we arrived in a village on the closure day etc. For me I want to enjoy the country, do side trips, stop if I find a great place to camp, etc. No conflict over the ultimate goal but totally different walking styles.
I meet and interact with far more people. It is much easier and more likely that a solo walker will meet people, share a meal or campfire than a larger group. This is particularly relevant when walking overseas.
Down sides:
Greater risk of accident or illness. That's why I leave a detailed itinerary and carry a SPOT which I use daily and have an agreed system of messages that means I can be picked up without creating a rescue. Being solo I also am much more careful and assess potential dangers more carefully - eg river crossings.
Loneliness. Usually quite happy with my self (I am a particularly witty conversationalist!

), and I carry music and books on my phone.
Can't do car swap trips - true.
"Perfection is attained not when there is nothing more to add, but when there is nothing more to remove".