So when I buy stuff, I want to use it for a long time.  I like the feeling of knowing that I've had something for a long time and it has always worked well.  Technology, even though it moves so fast, is no exception.  Consoles are a perfect example of this.  Not only I want a console I buy to work for many years, but I want their lifespans to be long.  I see a lot of benefits to consoles having long lifespans, such as: 

-The purchase is better justified.

-A better library.

-Developers learn the hardware very well and can create some impressive looking games.

-A greater chance for smaller IPs to make it onto the system (this one mainly applies to Nintendo consoles)

So I can see all these benefits to longer console lifespans, but I can't think of any benefits to shorter lifespans.  The only one I can see is that if a system is selling very poorly, ending its lifespan somewhat early can create greater profits.  So are there other benefits?  I named a benefit to the producer, are there any benefits to the consumer?

The only benefit I could see for short lifespan of a console for the consumer is if that brand isn't supporting the console that well with games. That brand might support a new console more. I still see short console life span as a negative thing to consumers in the long run.

Burying the shame ASAP of the previous failure.

It is not only better(for me at least) but also something that the console manufacturers will need to adapt.Development cycles are getting longer than previous generations.Today games usually takes 3-3,5 years to get made.Thats almost the whole lifespam of a normal console life.So i think that a 6-7 years for a console is not only better for us, consumers, but also a necessity

Better tech sooner.

- Lower prices of consoles
- Less risk for console manufacturers
- Smaller spikes in the cost of game production

That will never get utilized properly. 

To OP. I can't see any good whatsoever in having shorter cycles. 

The momentum can be pass over to the next console?

I don't like the idea of shorter life cycles. Like Nautilus said, games are taking longer to make, so a shorter life cycle would mean we would only see about one game per studio, per generation. That is not something I want to see. Even Call of Duty has went to three year development cycles. In many cases, developers have not switched to 8th gen gaming engines yet, and we are nearly 3 years into this current generation.

I think 8 year or 10 year cycles are perfect in todays market. Systems can get little enhancements in the non gaming aspects to keep them relevent, such as extra RAM for multitasking, faster secondary chips for better background networking and video decoding, and up to date Blue Tooth/Wifi/NFC wireless chips. But, I think the game side of the systems should stay at a set spec long enough to see 3 or 4 full games from places like 343 Industries, Turn 10, Polyphony Digital, Naughty Dog, and Guerrilla Games.

This will also mean each new console will see large gains over the last. It also makes things less confusing. Half of PlayStation consoles sales typically come after the 4th year, so I think switching consoles at a rate of like 5 year would just crush the industry by confusing the consumers.

The only people that really benefit from a short cycle are people with lots of money, people that need the best graphics all the time, or people that are living life trying to impress others with their material buying power. For the rest of us, and the entire game developement and ppublishing industry longer is better.

Lol, of course it will.