Reverse mountain range is used by most pirates to enter Grand Line. The other routes are Marijoa and Calm belt, these are not easily accessible. Why doesn't the Navy encamp at the entrance (or exit) of the reverse mountain range to capture pirates as they enter Grand Line?
Primary reason is because not all pirates are from the 4 Seas. Many pirates are hail from the Grandline themselves. If they are weak they leave Grandline and make themselves home in other parts of the ocean. A good Example is Arlong who left Grandline to conquer East Blue or Lola who escaped from "New World" into "paradise".
Navy also takes into consideration a variety of factors.
Pirates eliminate each other. Luffy didn't fight marines initially except Captain Morgan and then Smoker. He however eliminated other heavyweights of East Blue. Saved Marine the trouble. Thus stopping new pirates from entering the Grand Line may be proved counterproductive.
Shichibukai. The warlord system has worked well for the World Government. Pirates entering the Grandline are young and immature but only the strongest survive to reach the Redline. Thus The establishment of Marine Triangle near Sabaody Archipelago. They can stop the pirates their as well
Marines True Purpose. The true purpose of Marines isn't controlling the pirates. The pirates are dangerous because they are after the "truth". It is heavily foreshadowed that One Piece would reveal the details of Void Century and how World Government was formed. Hence the best of these are near the New World
Tenryubitto. The protection of "Gods" is also a much more important task. Hence we see Marine captains are of all types some of which routinely oppress citizens, are corrupt and don't care for the average people. Hence, the rise of Piracy and Banditry
The situation however is not completely like that. The marine implements what you've tried to ask. Try to think of the reason why Smoker was deployed at Logue Town. It was because being the last island before entering the grand line pirates would flock there to resupply before entering the grand line. We also see how he captures numerous pirates before they even enter grand line. A Logia powered captain can easily capture pirates worth 100 Million I believe.
To answer this we have to first look at the regions. We have the North, South, East and West Blue. The Grand Line, and after that the New World.
The navy has coverage in all of these areas to some extent but they can't be everywhere. Their army is not infinite nor is the bulk of the issue caused by pirates.
If you recall in the Sabody island arc (right after fishman island) not only was there a more heavy appearance of the navy but there also were way stronger members who were in the area.
Why? Because in the new world there is a higher priority due to several things (the tenryubito, the 4 yonkou, etc).
Naturally there need to be marines all over but they can't just set up a tent in one place. They need to be dispersed, but in a way where they have the bulk of their force where they need it most. Which is why the grand line is essentially uncamped.
Lastly, recall that it takes great skill to even cross the red-line most ships either crash into the mountain side or get devoured by sea kings either immediately before or immediately after crossing. I imagine the risk vastly outweighs the reward