It works. Players like to have that room to grow, and they can't grow if smothered with too much B.S.
There is nothing better than the party discovering some sort of detail that just works for them, but there are many cases where they have no opportunity to gain such information without a data dump. Some things just go to the grave with the player's antagonists. It's fine.
But sometimes, I like to give information. For example, I hope that every player knows how to use the to-hit tables and can calculate their own bonuses or minuses. It makes my game easier. In fact, I often have the players throw dice for even the monsters. It cuts down on paperwork, but sometimes it is an opportunity to give them a hint about something outside of combat.
For example, if two equal-level fighters are side by side, shooting arrows at a target and both roll the same number, both should hit or miss the target. However, this is a good place to drop a hint about other stuff. Obviously, two great fighting men should know how good they are. For example, someone might have a cursed weapon or a magic weapon. The target may have some magical device that only applies under certain circumstances like once per round. Once the party is aware of some weirdness, they can start ruling stuff out by logic, just like the real world.
|It's probably magic.|
There are times to hide some rolls, such as surprise or hiding in shadows. But even those rolls can give information.
One of my favorite tricks is when the party is surprised, I'll drop a die out of sight and say, "You hear a noise." Surprise is a surprise, there is very little you can do to mitigate it due to the mechanics. However, it isn't very fun to be surprised. By making that announcement and letting the party act accordingly, I am cranking up the pressure AND pushing agency to the party. It creates an environment of anxiety while allowing for possible (slight) mitigation PLUS it allows the players to set a standard of expectation that can easily be read.
For example, if a party thinks they are in an ambush situation, they may try to arrange themselves in such a way as to defend high-value players like Clerics and Magic-Users with meatshield Fighters and Rangers. On the other hand, if they never do this, you can set a different dynamic where those players are captured or incapacitated and the party is looking at a hostage situation rather than a TPK. It's up to the DM to receive the party's intentions or style and react accordingly.
One of my favorite experiences was a Thief who decided to sneak up to the walls of a fortification for a little recon. The whole party seemed to support the idea. I rolled for his hide in the shadows and move silently attempts. Each time, I rolled amazingly well. No one saw or heard anything. They were such good rolls that I showed the player the results. Obviously, these should have been secret, but they were so perfect so I decided to show her.
Then, disaster. The player of the Barbarian was having a little sidebar with another player when he suddenly realized stuff was happening and asked, "What's happening?"
Once the party explained the plan, the Barbarian nodded sagely and bellowed, "Look out! I can see you!"
Well of course you can see him. He isn't hiding from you, you twit.
The sneaking Thief got this "Oh, shit" look on her face. I leaned over and showed her that the dice indicated she was still not visible to the people on the castle wall.
To add to the merriment, I decided that the Barbarian's actions would be taken literally. The lookout on the wall answered: "Oh geez," and stepped back out of sight.
"How about now?" asked the lookout.
The party was gobsmacked. I gave them a few minutes to work out a plan. The Barbarian was drooling dumb and for once, his actual ability score matched the player's actions. The party adapted to the situation and everyone climbed the wall while the Barbarian offered unhelpful tips to the lookouts. No one intended this possibility, but damn it was fun.
You can't hide everything all of the time, but you also can't data dump on the players too much. Even if it is mechanical in nature. Also, you shouldn't try too hard to hide certain bits of data.
As a DM, you build a scenario, a story if you will, but you can't know how it will be received and interpreted. Information from the DM to the players is a fluid thing. You are effectively trying to merge the player's fictional actions with the player's visceral need for information. The DM needs to decide from the get-go what information is worth hiding and what is not.