Why in iphone impossible to turn off the sound of keypad buttons?

See here:

Product Feedback - Apple

Perhaps it would help if you explain exactly what you mean by "the keypad"? Do you mean the dial pad for the phone? The calculator keypad? Something else? If you mean the dial pad, are you asking about the DTMF tones? If so, no, you can't turn those off. You can, however, use the mute switch to silence them. It's the little slider over the volume buttons.

Old typewriter keyboards make sounds. Similarly, camera shutters make sounds, and the iPhone makes a sound when taking a photo.

”Why”? Apple has made its design decisions.

Do you mean Settings>Sounds & Haptics>Keyboard Feedback? You can chose sound and/or haptics.

Good clarification. I thought, perhaps incorrectly, the original poster was asking about the Phone app dialing keyboard.

See my answer above.