You may be able to decipher your unclear handwriting, but you probably can't read it as quickly and easily as you could if it were neater. Additionally, the right business hand ("hand" is the handwritten corollary to "font") would allow you to write much more quickly than you do now (in addition to being neater).
I highly recommend Write Now by Barbara Getty and Inga Dubay. It made my handwriting faster, clearer, less tiring, and (for the first time, despite my predisposition to RSI) pain free. For the 2 weeks of 10 minutes/day practice it took me to master, the investment was well worth it.
The handwriting taught in almost every American elementary school is a form of looped cursive. Looped cursive hands were not designed to be handwritten -- they are based on fonts designed for movable type printing presses. You see, in order to make movable type printing economical, printers needed a script with as few variations at the joins as possible, so they would have to stock fewer distinct pieces. Ms. Getty and Ms. Dubay researched how writing was done before the movable type printing press, and until you try it, you won't realize how much more efficient their cursive italic writing is.
As a side note, you would probably benefit greatly from investing in a decent fountain pen. A good entry-level pen will run you $14-20 US, last for years, and ink is incredibly cheap (a year's supply for less than $10). The advantage of a fountain pen, apart from price, is that it requires so little pressure compared to a ball point, roller ball, or gel pen. This reduces strain on your hand and wrist from writing, allowing you to write faster and more neatly.