For corporate business cards, I would like to remove the designation ahead of the phone number, if one phone number will be included on the card. Some cards will have both cell and work numbers, in which case those cards would have c: xxx-xxx-xxxx w: xxx-xxx-xxxx listed. For cards with one number is it helpful to still specify which kind of phone number it is? I like the look without it but can see that it is helpful for the caller to know, on the other side.
It's important only if it's important to the person that has the number.
For example, if it's their home number, maybe they want to make that clear (please don't call this number at midnight, as it's my home number!)
If you only have 1 number even without an ext, I would still assume this is an office number but that doesn't mean everyone will assume the same. One option you could go with is using a cell phone vs telephone icon if you do not want to use text. Personally I would add an indication for that 1 person who may be unsure.
No it's not important if you have only one number. It's up to you. If it's a business card people will know it's the office phone number and not the private home of the CEO! They know it's the number they need to call, it's on the card.
Often you'll see offices having 2 phone numbers and not mentioning they are phone numbers... It's more useful to specify it if there is a cell phone and a fax number, for example. And for this, you can use an icon or a letter (eg. P: phone)
But for an office, having only the XXX-XXX-XXXX is alright, as long you have the regional code or whatever you call these where you live!