In a word "No"
The physical benefits, speak for themselves, simply put it is better for your business if your website views easily on all devices and it doesn't mean you have to redesign your existing website from the ground up.
The often used business phrase "it's all about numbers" sums it up.
The facts are that "everybody" has a mobile phone, lots of people have tablets and the use of desktops as a % of total online devices is in decline.
The general trends are that on weekdays the PC dominates during the day, but in the run up to office hours (10am -5pm) during the daily commute then mobiles take the strain. Tablets are at the busiest during the evening.
If your marketing budget includes Adwords, directories, and referral websites then with the exception of newsletters, they are all responding to a users search term on Google.
So if a mobile phone user clicks onto a link to your website from the search engine results and finds large images and tiny text with horizontal as well as vertical scroll, it is just as easy to click back and select from the other search engine results which may have a responsive website suitable for viewing on the phone as well as on tablets and desktops.
Thinking it through:
If you had your IPad and your mobile phone to hand and wanted to access news feeds or your bank account which would you choose?
From Boot up:
Booting up a laptop or desktop is a pain - time/boring and if you have just closed down your office machine and freedom beckons the very last thing you want to do is boot it up again.
Booting up your tablet, be it Android or IPad is less of a pain, but better, whether at home on the sofa ( surreptitiously reading work emails or Facebooking) , in the local "wifi free" cafe or in the office for emails, apps and bank accounts and as they are battery powered and smaller they are less restrictive than desktops
Booting up your phone, well, only when it's flat.
Quality Experience.
Everybody wants a bigger telly benefiting from higher resolutions that eclipse that which the human eye can even discern the difference and this extends to work, bigger monitors for detail, concentration, expansive viewing (the 27" Apple IMac is a whiz, but ruins you for everything else) allowing multiple documents in the same view.
Convenience
On the go, in the car, on the street, the underground, broken down on the hard shoulder, Tesco aisle 23 looking for bread, in the pub, restaurant, at work, out on site, approaching Waterloo (standing room only) bleary eyed, just woke up, in the loo...
Taking photo's, videoing, phoning, texting, skyping, searching, calculating, sending money, receiving bulletins, email, ebay, Sugar crush candy, hiring cars, booking flights, music headphones, twitter, facebook, facetime, radio, spotify, stocks and shares, kindle, QR codes, on silent...
In your hand, handbag, man-bag, kitbag, jacket pocket, shoulder-strap, charger, hands free, bedroom table
24 / 7
Lost without it ...... the Phone wins hands down for communication.
Make sure your website is responsive.
You don't have to throw away your existing website, we can adapt and probably while we are it, add in those changes that you have been wanting to add to your website for a while now.