Oh heck yes, you would need detergent!!

You would need less of it because pure water is softer than the softest of tap water of course; ergo you will produce far more suds.
If you live in a really hard water area you always need far more soap or shampoo or washing up liquid to do whatever job is required than you do if you live in a soft water area.
the hardness of the water makes a big difference.
Pure water will not dissolve grease, for that you need detergent of some kind.
And Roger you muppet, all restaurants will use dishwashers (and not the manual dishwashers, ie, human staff!).
This way way they are rinsed and dried without the need for a tea towel, which is highly unhygienic

You're quite right about odour and smell though.
Ian