The Flash was invented in 1940. Quicksilver was invented in 1964. As the son of Magneto, Quicksilver was more of a sidekick / second class character to the comics. It is also impossible to believe that Quicksilver wasn't partially inspired by the Flash. Given that the comic industry already had a well established speedster to follow (The Flash) there likely wasn't much appeal to a new character with the same powers.
Why aren't speedsters more common or popular in general? It may be due to the challenges of making them interesting to the reader:
"Speedsters make me nervous, because if you play them accurately, they're impossible to beat...The moment someone sees him coming, it's too late. You shout, "It's the Flash!" and you haven't even got "It's" out before you're done...I could deal with Impulse because he was easily distracted." - Peter David (Young Justice)
There are also scientific challenges (Wikipedia Speedster):
The use of speedsters in fiction requires artistic license due to the laws of physics that would prohibit such abilities. Moving at the speed of sound, for example, would create sonic booms that are usually not heard in such stories. An enormous amount of energy would be required to sustain such speeds, and as some speedsters can actually move close to or at the speed of light, this would cause them to gain near-infinite energy, according to the laws of relativity.
In addition to Quicksilver there are other super fast meta-humans in the Marvel universe, they are just even less well known. Taken from the Marvel.com/Universe/
This list is not meant to be definitive, but rather an example to show that Quicksilver is not the sole speedster running around the Marvel universe.