Besides the Ice Climbers many chaingrabs, they also have the Ice Block Lock and Reset, Nana's Spike techchase, and Hobbling.
The Ice Block Lock is performed after Nana spikes the opponent and the opponent fails to tech. This isn't a true infinite, as the opponent can smash DI towards the edge to take less damage. It's also not guaranteed if the opponent techs the spike.
The reset is essntially the same as the Jab Resets from Melee. If the opponent fails to tech, a single Ice Block can be used to force the opponent to stand up.
Nana spike techchase, is basically doing throws into Nana's spike, then reacting to what the opponent does. It's not that useful in terms of chasing due the Ice Climbers' slow foot speed. They can get a smash in if they miss the tech or tech in place.
Hobbling isn't considered a chaingrab as far as I know, but it works the same. It is done by executing a throw with Popo, and footstooling with Nana. Immediately after the footstool, the Ice Climber player shoots 2 Ice Block, resetting the opponent. It's impossible to tech the footstool.
All of these can be done to all characters, just like the chaingrab.
Just like the chaingrab, it's extremely difficult to set up. The Ice Climbers have terrible grab range, and they have the second farthest skid animation in the game. This makes their shield grabbing game pretty bad. There are also no guarunteed setups for grabs. There are some that can work, like grabbing after a dysynched Blizzard, or after an Up-tilt/Squall Hammer. But the grabs are avoidable through DI. It's also difficult when all your opponents know not to get grabbed, and to kill off Nana.
Also, while a grab has potential to sweep an entire stock, the Ice Climbers are easily counterpicked by stages that move, like Rainbow Cruise, that makes it hard to keep Nana with Popo, makes it hard for the zero death to occur. There are also stages with insane hazards, like Brinstar, where the rising lava can disrupt their chaingrabs for a lot of the match. They also have trouble with stages that have platforms, or little space.
The Ice Climbers also have hard counters against them. Metaknight splits them way too eaisly with quick attacks and his range. His insane gimping ability makes it difficult to get an infinite off.
Snake has the range advantage on the Ice Climbers, and can camp the mess out of them. The explosives split the Ice Climbers pretty easily, and can help him from being chaingrabbed.
Rob has fast attacks, and multi-hit attacks that can split the Ice Climbers. His projectile camping/ledge camping is hard to get by also, and he's also good at gimping. He is also very hard to grab in general, because most of his attacks are safe on the block.
Pikachu is considered a hard counter too. He has multi-hit attacks that split the Ice Climbers up, and with the Ice Climbers' floaty nature, they are left as easier targets to thunder than most other character off the stage. Pikachu can also space with auto-cancelled aerials. His agility makes him tough to grab too.
Also despite the chaingrabs, there aren't any Ice Climber mains that are completely dominating the tournament scene.
This is my take on this issue. The Ice Climber infinite shouldn't be banned. The Ice Climbers are too easy to counterpick stagewise, and have a few hard counters. The grabs are also hard to set up on a opponent, due to their range, and no true way to set up the grabs.