Not sure how it works elsewhere but horse betting in the US is almost always parimutuel, meaning that everybody gets the post odds, regardless of when they bought their ticket. In other words, betting early doesn't give any advantage and in fact the later you can wait, the more accurate an idea you have of the actual payout odds of your bet. Thus, having access to a private betting machine, and not having to elbow other gamblers to buy a ticket at the last minute, is a real advantage.
That said, the state's take-out is so high in most states that you need a massive edge to actually make money. The slight edge a private betting machine would bring probably isn't enough.