In the past having a mobile look for a website wasn’t needed, in fact up until 20011 the percentage of people landing on website through mobile devices was below 2% for all websites we handle but this has markedly changed.
In the last three years the mobile devices landing on websites we manage has increased exponentially; currently the average website we manage has anywhere between 10% and 25% mobile hits, that is one every 4 potential customers. So if you don’t have a mobile look you might very well be losing a quarter of your potential customers.
Searching for mobile website looks that are available in the market you often find the oversimplistic almost text-only look, I think those are not only not attractive but they give the user the idea that 
the company is in the stone ages technologically. Think about it, people have phones with better screen resolution than most desktops, what they see should be just as good if not better than a desktop user.
You can see here two samples of mobile look I created for some clients, as you will notice they are made to give the user the full desktop experience in a tighter space.