When is Cyclometer useful? Some call it speedometer or odometer but I mean the thing to measure velocity, trip distance and such things. When you come up with a usage-case, please, point out the function which you use. The only thing where I may need a speedometer is to know when to lubricate e.g. after every 500km and to know the speed not to break speed limits. So very simple cheap one should be enough.

Not sure about terminology, whether speedometer, odometer or cyclometer. The first ones just return the cheapest units:  ~2.75USD (ebay) and 5.04USD (dx), perhaps Chinese are abusing the language or different English.
Speedometer = device which measures speed.

Odometer = device which measures distance traveled.

Cycle computers can normally do both (plus many other features you may or may not need).

Are they absolutely necessary for cycling?  No, but they can be quite helpful in many cases.  When riding long distances (e.g. touring, randonneuring), it's often important to know how far you've traveled, so an odometer comes in handy.  You may be trying to determine where you are on a map, how far until the next turn, how far to the next town, etc.

If you're training, being able to track your performance over time can also be handy.