We don't have a "do it all" class at all. This has been pointed out repeatedly. We have a versatile, customizable, general support class that can be decent in a few (not all) areas. However, a jack-of-all-trades was part of the bard theme consistently throughout D&D and has always fallen short of doing it all.
Earlier expertise, another proficiency, and reliable talent put them behind rogues in skills. Evasion and uncanny dodge put them behind rogues in defense. Cunning action puts bards behind rogues in action economy. Sneak attack puts bards behind in damage. Bards are behind rogues in combat and a bit behind them as the skills class. This is mildly ironic because skill benefits are what bards get instead of spell or combat improvements like other classes.
Bards are far beyond most classes in direct combat. They do not have the hit points and armor other classes have and when they lean towards those directions it's still catching up to fall behind. Fighters, barbarians, rangers, paladins, rogues, monks, and clerics with domains moving towards melee are all beyond bards in combat. A dwarf wizard with shocking grasp is above bards in combat. Bards are about as low end can go given their one poor damage cantrip and light armor and lack of defensive spells.
Magical secrets doesn't exist until 10th level, and true to arcane casters picking up spells outside of the list they count against spells known. That's a long time for what amounts to a small perk because the bard still didn't gain any way to increase the power of those spells and he's still limited enough in options that he has huge opportunity costs. The only way around that is with the lore bard, and continuing to really suck in the combat pillar outside of support.
Bards can pick up medium armor (and heavy by feat if they live through the first few levels likely dumping CHA or starting at a higher level). They can take feats or spells to help with their extra attack after doing so. That builds them up to mediocre damage without other class abilities bolstering their combat (because they get skills and support in the chassis).
The bard can go lore, which gives them more skill focus instead of spell power and the ability to debuff with inspiration so decent, and even pick up eldritch blast plus hex as an example of damage. Again, it's still mediocre in comparison to warlocks, or evokers, or sorcerers using points, or melee damage we see in those other classes. It's an investment to improve and fall short. It also means that lore bard obviously isn't also taking fireball or paladin smites because that's not possible. There are far too many Shrodinger's bards in these discussions where the bard seems to have more secrets than the class gives secrets. On top of that, there is far far too much competition for concentration on the bard list for hex. They'll lose it to a failed check on damage or because buffing / debuffing usually needs concentration.
It doesn't make any sense to pick up a small damage boost with hex and give up the concentration on a more impactful spell. Bards do have some good spells. Those good spells are in the support / control style.
Bards can be good healers. Not life cleric good but good. This requires using the lore bard's extra secrets to pick up 2 out-of-class spells. They can still be decent enough healers but well behind clerics and druids without those 2 secrets at 6th level. Again, that means they are not picking up damage spells, defensive spells, or "poaching" class niche spells. Because that's still Shrodinger's bard logic going on. They cannot do both at the same time. That's one of the reason's they can be decent in multiple areas but any move towards one area is simultaneously preventing moves to another.
A bard does not get revivify or multi-target healing until mass cure. Those do not exist on their list and that keeps them behind. They can rely on heroism (taking away the concentration slot), which incidentally would be very iconic of them for inspiration. Taking healing word, heroism, lesser restoration, mass cure wounds, raise dead, and greater restoration is half their spells known just for healing at that level. That actually leaves them with 6 spells for combat, defense, and utility at a time when sorcerers would have 10 spells to cover those areas.
I want you to think about that and let it sink in. Bards have less spells known for other areas than sorcerers do to try to cover what the sorcerer would because bards are also covering healing and that wears the resources thin. Bards aren't like clerics and druids where there are a plethora of prepped spells so and that stops them from covering too much at once. The sorcerer has more to work with after healing plus metamagic plus bloodlines than enhance magic. On a side note, that's also probably why sorcerers feel like they have plenty of spells known when I play them -- not having spells known given over to healing as I spread thin on a bard feels like I've got plenty at that point on a sorc.
Song of rest is a nice bonus, but it might actually be the only healing the bard even has. If a player wants the bard to do more spells of other types, those spells known have to come from somewhere and that often means dropping healing spells. I have done that (although I added the healer feat because I couldn't give up the expectation of some healing).
Being able to "do everything" means to a degree. That degree is always behind more focused classes for a bard and working on one area is always neglecting another. 5e hasn't actually changed that. Bards have a lot of options but they don't actually get to take them all, and that's what people seem to be missing.
Now if that doesn't feel "right" to you, that's fine. Just because that's how bards are designed in 5e doesn't make them for everyone. I'm giving feedback on your "do everything" comment because that looks like you don't have the experience with the class tbh. They really are just a solid support class (which is what I think bards should be) that can be decent in a few areas of focus.
Hopefully my experience gives insight.
