I think everyone is just assuming the Ranger is bad at level 11 and aren't doing the math. The Paladin gets +1d8 "on every attack". That is 2 for a great weapon fighter, which is almost universally agreed to be the biggest damage dealer. So that is an average of +9 damage if both hit, and it is only for melee attacks.
A Beast Master Ranger gets an extra Animal Companion attack that does 1d8+5 (with 16 Wisdom), which is an average of 9.5 on a hit. Plus Hunter's Mark if they have it up (and with my house rules, they will).
A Fey Wanderer gets Fey Renforcements with gives them a Fey Spirit that deals 2d6+6, with Advantage for Fuming, for 13 damage on a hit. That is a bit more, but requires a round to set up. Plus another +1 damage per round for the increased (and much maligned) Dreadful Strikes. After four rounds that is 42 damage vs. the Paladins 36, and that is assuming the Paladin was actually able to use it on the first round and didn't miss a round of attacks closing or using throwing weapons which don't get the bonus.
A Gloom Stalker's Dreadful Strike (Same name? Almost) does an extra 2 damage at level 11 on average, and they can either get an extra attack against another creature (either 2d6+5 for a two-handed weapon for 12 damage or 1d6+5 for a light weapon for 8.5) or they can debuff all creatures in a 10' emanation from his primary target with Fear. So even with a light weapon that is an average of 10.5 damage or they use the fear effect. It's not single target damage, but I know my group rarely only has one opponent to fight.
A Hunter... Okay, the Hunter sucks. It is just 3.5 damage to a creature you are not focusing on. There is no attack roll or save, but it still sucks.
The new Winter Walker gets a Reaction to Stun a creature that hits them. Which they can do a number of times a day equal to their Wisdom. This is an awesome ability that is hard to put absolute numbers on, but it can doom an enemy if it sticks as the rest of the party murders them while they can't move with Advantage on every attack against them.
So yeah. You have to be careful about adding more damage to the Ranger. They really aren't that far behind (except the Hunter). The only way the Paladin stays ahead is by burning through spell slots to keep smiting. Rangers have more interesting things they can do with their spells in my humble opinion.