Nasus is a great late game champion if he can safely farm. The main problem with Nasus is that he is countered by a lot of champions. In lane his main worries are Gangplank, Gragas, Irelia, Lee Sin, Nidalee, Renekton, Ryze, Skarner, Tryndamere, Udyr. They all have to ability to be aggressive on you. Unfortunately, Nasus is not very good at applying pressure back and this usually leads to a lost lane. Nasus also can be easily kited in team fights.
Nunu has great sustain in lane and can even harass a little bit with his snowball. He also has a speed buff to make escapes and two different ways to slow the enemy (on being AoE). However, there is one major flaw to AP Nunu and that is he is not very useful in team fights. His snowball may be good for poking and harassing. But since it is on a 6 second cooldown, it can't deliver consist damage in a teamfight. His ultimate is one of the best in the game if it connects. But most league of legends players know to cancel your ultimate with CC or can escape from it. Essentially, AP Nunu is a support with no constant damage for team fights and bunch of gold from lane that could've been used on a different champion.
I'm not too familiar with Volibear so this section may not be as accurate as the Nasus and Nunu sections. Volibear can be good in lane against some champions. His passive makes his enemies commit to him thinking he is low in health when really he heals a ton back. He also provides a fear and a throwback similar to singed. However, Volibear has to get into the enemy's face to deal damage. Which wouldn't be a problem if he wasn't kited easily. He has trouble against ranged champions who can keep him far away. His cooldowns on his abilities are fairly high (the lowest being 8 seconds on Rolling Thunder if you max that skill first which you most likely won't. Otherwise it's 12 seconds if you put one point into it.) Enemies can literally just walk away from his ultimate if you don't have you abilities ready to CC him. Finally if Volibear doesn't dominate his lane, he can fall off late game and be kinda useless.
Final Note: All of these champions can be viable for competitive use if played correctly and against the right champions. Nunu can out poke the enemy champion and shut them down in lane. Nasus and Volibear can be played if they have the right matchup in top lane. For this reason you never want to pick these champions before you know who the enemy's top lane is (Nunu is a little safer to pick because you can always just play him in the jungle or support). It all comes down to the picks and bans.