Such spineless behavior should be punishable by law. If you do not have the courage and decency to tell someone they are worthless to you as a business asset, you have no right to run a business or be involved in any kind of decision making process pertaining to business.
Sending a text message is very impersonal, and to use it as a means to fire someone is just cold. If you feel you have the grounds to terminate an employee, then you should have no problem facing them in person and telling them to their face. They need to be able to appropriately respond to any claims you make, and texting just isn't sufficient.
No, texting is not an appropriate way to fire an employee. Hiring and firing are significant acts that warrant a face-to-face conversation. An employer should have the respect to let an employee know what is happening rather than just shooting off a text message as if it were a careless, inconsequential act.
No, it is not appropriate. Employees are not allowed to apply for work over text, generally, and therefore important matters such as terminating an employee's job should not be handled over text either. It is unprofessional, impersonal, and somewhat disrespectful. If someone is being fired, then face-to-face is the best policy, if at all possible.
Texting to fire an employee is the most passive aggressive thing I have heard in a long time. It is totally inappropriate. There is no circumstance where it would be ok to fire someone in this manner. Terminating employment must be done in person, and should never be done in such an unprofessional manner.