No not really. If an interrupt is successful and I was being ganked, it doesn't make it less useful. Cast time on most item except potions aren't zero. If you fail to use teleport you won't likely to be able to use it again even after interrupt due to 3s cast. The interrupt time is long enough for significant damage to be done.
Depends. In 3s I could get off a couple of AA hits and a skill. But chances are my other damage dealing skills are on cooldown if the enemy is low enough on health to use a tp scroll and I used an interrupt instead of finishing him off with my primary damaging skill.
It does not induce cooldown on abilities then why should it induce cooldown on items.
With your argument you can argue interrupt is useless cause I can cast my ability right after I was interrupted.
Interrupts do induce cooldowns on abilities. If I foul grasp a Sedna about to use heal she won't be able to use it until the cooldown is up. And with a cast time of 0.5 seconds interrupting heal would be fairly pointless if it didn't induce the cooldown.