you cant pick all 3 subclass as bard as well, so no, you cant do bard caster and melee in 1 char xD xD xD, so other classes are better than bard in one specific build archtype
show me bard who can aoe all stell watch in act 3 in one turn or kill elder brain in one turn as melee or can burst so fast as paladin with smite or do so ridiculas single damage as fire sorc
bard cant also cast haste on 2 characters or stone skin on 2 characters or even resistance shield on 2 chars,
bard dont have op shit like dual cast speed cast or paladin smites for ridiculas burst, even light cleric do better magic damage than bard and can also do some support and heal
Oh, but they can melee, ranged and spellcast - it's called sword bard.
And you are picking situational stuff - if you talk about twin haste then it's a sorcerer, a sorcerer can't attack twice with double crossbow, is not good in meele - and guess what, a sorcerer can't smite either. A paladin can't buff enemies, apart one or two smaller buffs, or put them completely out of the fight with Ottos irresistible Dance or Hypnotic Pattern. A light cleric might have fireball as a good AoE, but guess what? Magical Secret can give any bard subclass fireball. All bards can crowd control, have decent attacks, granted, lore should stay more in ranged, but are beasts with double crossbow, all bards can heal and buff, all bards have de facto a third short rest, all bards .
People trying to explain to you, how a bardworks, but you don't get it. No, the bard is not the best in anything (but speech checks), but they can do anything. They are the most versatile class in DnD. While the other classes can do mostly one or two things good, a bard can do a lot of things. They are even proficient in any skill with Jack of all Trade - they get bonusses of all skills, they are not proficient with. Only githyanki can become as close as that in terms of skill monkey and they have to decide every day, in which skill set they want to become proficient, while bards just are. A performing bard is the best distraction, if you want to send your rogue stealing, without the crowd noticing.
And in terms of being powerful - maybe watch the video, victor linked above, you conveniently ignored that.