Sure and I think that is how 1E was designed.
Only arguably - and then only post Unearthed Arcana. Without Weapon Specialisation fighters suffer badly against clerics.
I don't think the PHB ever says or suggests all classes are equal and I for one have never assumed they were.
What is the purpose of levels other than a measure of power? What does challenge rating imply other than that characters of the same level are roughly equal in power.
In TSR era D&D this was counteracted by different classes levelling up with different XP. But at least from 3.0 in 2000, more than 20 years ago this has not been the case and challenge ratings that are supposedly equivalent and that just rely on PC level for balance without mentioning class have been a thing.
Cosnidering all three phases of the game and with Tashs's new rules Rangers are mechanically more powerful than Barbarians, Paladins of Fighters. Old stereotypes die hard and there are lot on this board who look to the PHB Ranger which was underpowered compared to these classes.
Rangers are mechanically more powerful than barbarians and fighters. This is because they are roughly equal in combat - but without spells or significant non-combat abilities fighters and barbarians alike are glorified commoners at any problem where the solution isn't to hit your foe until they stop moving.
The thing is that the PHB ranger
wasn't significantly underpowered compared to the PHB fighter and barbarian. The Tasha's ranger didn't gain much, if anything, in the way of damage abilities. Favoured foe is still probably weaker than Hunter's Mark and doesn't stack with it.
What the ranger was was hard coded with no room for shenanigans. A sixth level ranger knows four discretionary spells. Every single pre-Tasha's ranger I have ever seen made their first spell Hunter's Mark because they needed it to keep up with their damage. They made their second spell healing because it is that useful (normally Goodberry, occasionally Cure Wounds) and they wanted to be a team player. And they made their fourth Pass Without Trace for exploration or Spike Growth for combat. Leaving not much.
Now? They have actual spell variety and customisation. Their combat hasn't improved (indeed some are worse thanks to no Hunter's Mark). But with things like Expertise and the rest of Natural Explorer, Beast Sense, and Beast Speech they are the explorers rangers should be, rivalling the rogue, and still hold their own with the other martials in combat.
And paladins are just fine. They nail the combat pillar, including having the best saves in the game and are high Cha socialites with healing and spells to support them.
The class that really lags because it doesn't scale is the barbarian. They're awesome at tier 1 - but Rage falls off badly because elemental damage becomes much more common at high level. And the Barbarian level 11 "mini-capstone" will protect you from three papercuts. It looks a lot better than it is.
Rangers are a class who gets extra attack and has nearly as many spells a day as a full caster while also having more skills, expertise, class abilities, d10 hit dice and top notch subclass abilities (on the better subclasses).
The thing is ranger spells are lower level - and they only get "nearly as many spells per day" if you count the very situational Beast spells. So they are nowhere near as good at casting. Rangers are able to hold their own with casters because they are half-casters with a huge grab bag of abilities. But they aren't notably good compared to full casters. The non-casters need to be brought near their level.