There's always lots of work for artists who can emulate styles and break down the differences in order to produce products. Art in the grand scheme of things has always been about that. Even the great artists worked for commission. Michelangelo (and the other renaissance artists) in particular never worked alone, but with entire teams of people to help them paint or sculpt their grand works.
However if you're looking at fine are a distinct style can be everything. If you can make worth that resonates with others and stands out from the crowd then you can go really far.
I do find though that those who focus on style for their own gain often are either too inexperience to know that they need to work on their fundamentals more, or they've lost sight of why they're making art in the first place.
So is it important? Yes (if you plan to sell your work), but the basics are more important for artists both pro and hobbyist alike).
I'm really on the fence about style. I think while you're learning, style should be the furthest from your mind. Try everything, make ugly art, really get dirty and find what you like and what you don't like. Style is often a term used instead of skill. "This is my style." Nah, That's your skill level.
Popularity isn't what's important. Exploring and finding things that interest you and diving into those subjects for no other reason than YOU love it. That's what gains you attention. Showing how interesting you are through the things that you discover about yourself, is what people enjoy most about your work. That passion and drive, appears in the work that those people do. Sure they got famous or there's a "style" but really you recognize the marks of their personality all over the canvas. And all of those masters were really interesting people. That passion is what drives people to excellence, not the need for attention.
beeing recognizable is different/not the same to beeing real - i truely prefer the secound... getting famous is a very unpredictable thing - and its a pitty so few artists can make a decent living from their artworks. but getting stuck in a certain way of arting only because of having a signature style is not what i wonna experience with my art! i guess, everybody has to make this decision for themself...
For me, my art is a personal event that expresses the essence of my Being and/or intent. The signature is a representation of the personality of the artist while also making a 'mark' that is individual and unique. A mark that is recognizable and consistent.
The use of a signature is a means of identifying the art and style of the individual artist. It is a personal thing and is not only important for the artist but also those that acquire artwork. In many cases, it is the signature that sells the artwork.
While in a restaurant, Picasso signed a napkin for $20,000. The signature, like the artwork, is a personal event.
In bead work, often the signature is a bead placed in a certain way that stands out from the others. When creating art, the artist creates a universe that is specific to the life and inner self of the artist. As an artist becomes more and more skilled, the signature becomes more important not only for the artist but for those who may recognize and appreciate the skill and technique of the artist involved.
In time, just the technique of the artist can be recognized and, in a way, a signature in itself. Van Gogh is an excellent example. His style was so unique that his work can be instantly recognized.
It's extremely important if you wanna be good and popular. But getting one requires an ungodly amount of stressful, soul-crushing studying and *shudders* leaving your comfort zone. Provided a bad drawing doesn't make you wanna quit art forever, you'll be set.
On a less cynical note, you can also look at other artists you like and learn how they do things.