Maybe you should read "Flash Boys" then.
They can and do.
Orders start at one place, and by regulation then can get sent to many other markets. If you can go to those next markets a little faster, you can front run the order.
Flash Boys uses a totally fabricated use of "front running". It's worse than people that call copyright infringement "theft". That book is probably one of the worst books I've read as far as accuracy goes. At least that I'm aware of.
Seriously, at one point, Lewis suggests that the trading station of some big trader is hacked. That just by typing numbers without submitting an order, stuff jumps. This should send huge red flags off on anyone that's even remotely familiar with anything similar to a computer. But it's another "see how rigged it all is?" anecdote blended in with his nonsense.
Some programmers don't understand latency, so there's no hope for anyone who's not familiar with software development to wrap their head around the concept of "yes, things happen in milliseconds".
Which makes it all the more easier to get away with anything that sounds as sensational as this.
https://www.amazon.com/Flash-Boys-Insiders-Perspective-High-...