It may be quick to use poor handwriting to get all the paperwork done, but think of the day you get subpoenaed, and your poorly written handwriting is blown up on a screen for the courtroom to try to read. Imagine the lawyer making a case that because of your poor handwriting, information was either mistranscribed or missed altogether causing poor outcome. Poor handwriting is no longer a joke or an excusable fault in this day and age of lawsuits and audits.
Taking an extra few seconds to make your handwriting clear not only can prevent errors, but it will also endear you to the staff who have to read the writing. Doctors may think they are the only ones who are busy and work blistering hours, but actually there is a whole treatment team involved in patient care who need to read the info the doctor writes. None of them appreciate having to spend their time, which is just as valuable, deceiphering poor handwriting because someone considered themselves too busy or too important to make an effort.
Good handwriting, along with being polite while on call, make a huge difference to the staff on whom you depend on to carry out your orders.