Pinned is better than prone. Prone provides disadvantage for all ranged attacks while Pinned provides advantage. Considering how awesome ranged rogues, ranged fighters, and ranged spell casters are this is not something to dismiss out of hand.
Advantage counteracts disadvantage so you don't have disadvantage to attack the target you are pinning. What it does do is take up an attack. This is where the synergy with Battlerager armor comes in. You get to do damage to your target while your entire party gets to do a lot more damage because you have them pinned.
You will never be as useful grappling a creature as a monk would be stunning a creature, but having Pin is close; if I were to rank them, I would say Stun > Pin > Prone.
On the subject of safety you are not likely to grapple unless you are fighting one big target and if it is one big target the pin provides you some safety. You can also rage for additional resistance to physical damage.
Again, there is no pinned condition. What you are referring to is the restraint condition.
And yes, advantage counters disadvantage, as I have already stated myself. That means you get nothing out of this situation yourself, apart from having disadvantage on Dex saving throws yourself and having a speed of 0, both being bad. Both you and the target treat your attacks against each other as normal. Your ranged fighting companions might get some mileage out of it if they insist on fighting at range, but so do any other ranged fighting enemies against you.
Even if there is only one villain, who can be grappled, the 5E system is flexible enough, so any rouge, ranger, fighter, or whatever, even when normally leaning towards ranged fighting, can still draw and reliably use a melee weapon. They are not bound to using one weapon always and only, as it had been with the 4th Edition. Even if they picked the archer fighting style, their melee capabilities aren't crippled, and don't forget advantage. So they can also easily take on a proned enemy, while being able to apply most if not all their class features and buff spells (Sneak Attack, Colossus Slayer, Hunter's Mark, Hex, etc.).
Clever spellcasters can use spells like Spike Growth or Cloud of Daggers, which you can drag your grappled target into for additional damage. Spells, which require a saving throw are working as normal, but successful Shocking Grasps are great as the proned target can't use reactions until the caster's next turn, so he can't OA any companions, who hit and run. Flexibility isn't a one-way street, and 5E is made to be flexible even for archers or spellcasters. It's up to any player to make use of it, though.
But Fighting only one big solo target is a rarely the occasion, and even if, it might be a huge or larger target. Then you'll have to go into basic melee anyway, except for using a potion of giant growth before taking on a huge creature. Apart from that most encounters still include henchmen apart from a major villain.
So instead of your ranged party members picking on your target, they might instead go for any ranged fighting enemies or spellcasters, which you do not have the speed to engage and grapple right away. With that they might keep you from harm, while you are shutting down those melee combatants, which otherwise might threaten your squishies.
You should rage as a barb grappler anyway. The Grappler feat is redundant, as there are better and less situational feats available, granting more significant benefits and don't forget you also need some ASIs. It surely does not belong into an optimized build.
