New kitchen sink waste

I'm about to fit a new sink and to give me a less cluttered cupboard, I'm thinking of not fitting a trap directly under the sink, but running the waste pipe down the wall at the back of the sink unit, through the floor and into a cellar where I can fit and service a running trap and then connect it to the existing exit route.
Is there any reason why I can't do this? What do the experts think.

Trouble is the inside of the waste pipe above the trap will quickly acquire a coating of grease, soap scum and food waste, and it will stink!

Best compromise is probably a 'space saver' trap.

They fit flat against the wall behind the sink, and link to the sink waste outlet with a telescopic section incorporating a double bend.

The version above is for a 2 bowl sink, but others are available for 1, 1½ and 3 bowl sinks, plus inlets for washing machines, dishwashers etc.

You're right. This does look to be a good compromise. Thanks