I've always liked single shots, not just Handi's but other makes too.
The way I was tought was that if you need a follow up shot that you should learn to shoot better, use a more suitable caliber/cartridge, and better designed bullet-or dont take the shot. The single shot available makes you more likely to place a better aimed shot, one more humane to the receiving critter. It takes more skill to use a singleshot, then it does to use a rifle that you can let you sling 4-7 bullets thru the air in 15 seconds.
My first years hunting were with my dad's Win 94 30-30. But he only gave me one bullet. He said make it count.. ..since that very first outing, I've never ever had to pull the trigger on the same game animal twice.
Lets not overlook the fact that these NEF/H&R's and Rossi's comparible models are a godsend to us poor people. Not all firearm enthusiests can afford to shoot targets regularly, let alone own a high dollar firearm.
I've owned MAK-90/AK-47's, AR-15's, Marlin Camp 9/45's, leverguns, boltguns, and pumpguns.. ...all but my Marlin 93 levergun are gone. But I still have my singleshots, they perform as well as several hundred dollar multi-shot rifles-the proof is in my freezer.
I still have my Mossburg 500 12ga and my Marlin model 50 or 60 22lr semi rifle though.. The 22lr for plinking cans or teaching my younger cousins how to shoot, the 12ga for turkey shoots and hunting. The Mossburg will get replaced with a hammered double shotgun someday..