Triggered abilities are not activated abilities, the two are very different. Why do so many people treat them as if the terms were interchangeble? They are not. They are precice terms used in the Magic vocabulary with very specific meanings. Only activated abilities can be activated, only triggered abilities can trigger.

An activated ability ALWAYS uses the template [cost]:[effect], either on the card directly, or in the rules if it is a keyword ability. If an ability does not have that template, it is not an activated ability.

Triggered abilities ALWAYS denote their trigger conditions with "when", "whenever", or "at". If an ability doesn't, it is not a triggered ability.

So of course Nahiri's Binding does not stop abilities from triggering. They are not activated abilities, and you could not activate them if you tried, even without the Binding.

Card seems to keep being playable.