Although the old style schutzenfest rifles were single shots, I don't think you see any single shot rifles in competition these days, do you? At least not Ruger No. 1s. And the are not necessarily less expensive, given what a Ruger No. 1 goes for or one of the modern day Sharps rifles. The difference is in the finish and the wood, I'd say. So, other than the shorter overall length for a given barrel length, there's no real practical advantage.
A curious thing about the owners of single short rifles is they way they will tell you that you only need one shot and how you have to make that shot count, then turn around and boast how quickly they can get off a second shot. To be honest, I can understand both statements, having owned a few single shot rifles when I still was shooting rifles. One really can get off a second shot fairly quickly with at least some single shot rifles, even when running (yes, really), though more than about three shots will be getting a little difficult unless you're holding cartridges in your mouth.
It compares fairly favorably with some Mausers that have a relatively stiff action, but not so well with something like a Lee-Enfield. Of course, no manually operated rifle will compare well with a semi-automatic and those have been used for hunting since the 1930s.
I have two Ruger #1 rifles that I've used for 30 years. The #1 was used and admired by Elmer Keith as the "finest example of a falling block rifle made."
Now, that is not a reason to own one - but it does show that a noted gun authority liked and used the single shot rifle.
The #1 is neither right handed nor left handed - it works the same from either side. That's an advantage for left handed people who don't have the money for a left handed bolt gun.
The gun is simple to accurize. With a #1 you free float the forearm of the gun free of the barrel so it is only attached by the barrel hanger - and then seal the wood on the inside of the forearm that has been relieved from barrel contact. No glass bedding required. Free floating requires two pieces of equipment. A dowel about 3/4 inches in diameter and a piece of 220 grit sandpaper. No need for glass bedding and all of the other techniques used for a rotary bolt rifle.
If you are careful with reloading - you can neck size only which improves accuracy as the brass has been fire-formed to the chamber. You don't have feed problems as you don't have a repeating rifle.
The #1 action is extremely strong and hot loads are not a problem in the gun.
Now the question - why do I have a single shot rifles? One Ruger #1 is a 6mm that I use for prairie dogs - you don't need follow up shots. The second is a 30-338. This is a custom round and was simple to make in the Ruger #1 by changing the barrel with no other work to the gun required.
How you do follow up shots with a Ruger #1? It takes practice and if you don't want to do that - don't buy a #1.
If you do want to take follow up shots you hold the cartridges between your index and middle finger, and middle finger and ring finger in the hand that feels most comfortable for you. I use my right hand as I'm right handed and can guide the new round quickly into the chamber.
You rack the lever open, the spent brass is ejected and you push another round in - not quite as quick as a box fed rotary bolt - but I've never missed a follow up shot using that method.
If I need more than that - I'll load a 20 round magazine into my Les Baer .308...and forget about bolt action rifles completely as being far too slow with not enough magazine capacity.