Above Threshold Training. Why do it?

Working on your VO2 max effort intervals creates room for threshold improvements.  Lets say a brand new cyclist starts out with a 1 hour max power (threshold) of 200 watts and a 5 minute max power (VO2 max) of 275 watts.

If that cyclist has a goal of eventually getting their 1 hour power up to say 250 watts, then most certainly their VO2 max will have to rise as well.  If all you do is threshold workouts, yes, your VO2 max will also raise naturally, but the point is that until you reach your genetic ceiling for VO2 max, you should always spend some time working on it if you want to also reach your threshold potential.  

It's not to say that triathletes need to use VO2 max efforts while racing (as compared to bike racers), but just because it's not used during racing doesn't mean it's not applicable to bike fitness.

And since pictures, tables, and charts can really help. Table 1 defines the zones and Table 2 shows the benefits of each. There are a lot of things listed there, but look mostly at Increased Lactate Threshold and Increased VO2 Max. You do work VO2 max some in zones 2, 3 & 4, but the most benefits come from Z5. Above threshold.

No. Gains will be more limited, but could still be notable at times.

Some training above threshold can help you make more gains. This is not all or nothing, but understanding various aspects you are trying to work on.

No...pretty sure nothing in my post said that so I have no idea where you got that from.

As brigby mentioned, it's not an all or nothing.  Building bike fitness is a result of ALL of your riding.  Even the easy stuff where you're riding at conversational pace.  Riding at various levels stresses different parts of your fitness (as linked by brigby above) so it is beneficial to work on all those areas if you want to raise your fitness as high as possible.  

Again, the point being that just because a triathlete will almost never use a VO2 max type effort in racing, it doesn't mean it's those type of efforts in training will not improve their overall bike fitness and their ability to raise their threshold power (which is more applicable to triathletes).

Word!

It works for running and swimming too.

It depends on the distance you are racing and your proficiency/level of fitness. Usually about 5 or 6 days out from a race my kid does a wicked fast triple brick workout with short efforts well above his threshold.  It sets him up well for a race.

Yes, and I also like to do some above threshold work in that same time frame. Especially for short course.

As was stated above in another post a lot of times VO2 work is done early in a program (raises the roof) then morphs into threshold (critical power) workouts (raises the ceiling). For instance take a look at the BT winter cycling training program.  There are 3 distinct phases which in the beginning versions were called VO2 Max (now Improve Maximum Aerobic Capacity), 20' max power (now Improve Slow Glycolysis) & 60' max power (now Improve critical power).  I personally find VO2 and the middle phase (e.g. 6x4', 4x6', 3*10') type workouts easier.   I dread the  3x15', 2x20' CP type workouts unless its 50*F in the garage, but they but the hair on your chest!!!

Well, it depends how you structure the intervals.  If you were shooting for your typical threshold level 20' intervals to begin with (at roughly 90-98% of threshold power), then you're going to be pretty shelled after those 20' intervals.  Likely you won't be able to do those 2' intervals at the end at a VO2 max type level (110-120% of FTP...considering it's only 2').  If you can, you probably sand bagged the 20' intervals too much.  

But if you plan to ride the 20' intervals say at tempo-ish power (83-88%) then you probably could pull off the 2' intervals at the end.  

I wouldn't say either workout is "better", but it's just important to keep in mind what is realistically possible.  60-90 minute interval workouts generally leave you wiped out at the end if you did it right so when deciding what intervals to do, you have to allocate how much energy you want to use up for each interval.  It's nice to say that you will shoot for 2x20' at 100% threshold power and then do 3x5' at VO2 max power to finish it off...but realistically it's not possible.

But if you did the 2x20' at 85-90% then you can do some interval stuff afterward. E.g., the following is a sweet spot workout with some short 30" intervals at the end. This one was right before a test week and it's apparent based on the intervals that I needed a bump in CP to make the workout a bit more challenging!

As always, it's what you want to get out of a session. When multiple aspects are pushed in the same session it's quite likely no one aspect will be maxed out before exhaustion sets in. Doing a set with 2 x 20' up in the high 90's and then some couple minute intervals up in Z5 is possible, but does take some training to be able to pull off. And no part of it feels "pleasant".