The use of a keyboard is a very good question. The use of the remote control just like you'd use a mobile phone to get text and numbers onto the search bar is a software function decided on by YouView. It uses matching to get results up with the fewest keypresses so it normally doesn't take many remote control button presses to get a result. So, YouView chose not to incorporate an on-screen keyboard.
The TV box is compatible with some USB connected keyboards and although I haven't personally tested the seach function I think it ought to work. The external keyboard is part of YouView's remit to make the product accessible to as many people as possible.
YouView are also testing with the Smart Home Hub / Assistant / Speaker devices like Google Home or Alexa so the YouView TV Box can accept voice commands for the Search function.