Uh yeah! Cuz they are H A R D! Kudos to you for choosing to face the pain with old school classic 4min 120% intervals!
Do you fail on the first interval or on the last? If it’s on the last, that’s probably ok (see above); just do that last one until failure. If it’s the first then it could signal a couple different issues. Maybe you are going out too hard. Think of the entire session like one big interval. If you start off too hard you’ll never make it to the end. Could also mean you just aren’t ready for those long killer intervals yet. Tone it down to maybe 3min reps and let your body — legs + lungs — work it’s way up to 4min (or even 5min!).
Ha! Many a pro and amateur rider have said the exact same thing. At least you know you are operating at/near your VO2max!
The hardest, probably. The most gains…in dispute. The gains come from time spent working in your VO2max zone. Don’t forget, VO2max is a physiological function, not a power target. Intervals that push the heart rate to >90% max are the most effective, regardless of power. If you can’t finish your interval, then you aren’t getting that time in zone. Have a look at something like Rattlesnake or even a standard session with shorter intervals.
Good luck! 