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Chaelexi
You can always play WoW without buying the latest expansion set. I don't see why anyone would do so after they hit the current max level but buying expansions has always been optional. I can't see why this would be any different with classic servers. That's of course if we assume classic servers are linked to regular subscriptions instead of being independent monthly fees or even B2P costs.
The original question was if you can level from 1 to 60 without grinding mobs for no other purpose than to get exp. I know the answer, yes you can. Running dungeons is part of the usual gameplay and doesn't count as grinding, does it? Besides, there's nothing wrong in mob grinding, lots of people do it voluntarily, even like it, some even prefer it over quest grind. I, for one, want to level up my professions as i get levels so i sometimes stop to grind mobs for cloth, leather or meat, not to mention times when i'm broke and need some gold for something in the AH or maybe mount and need to grind some gray drops for vendoring.
There's no correct or wrong ways to play WoW or any MMORPGs for that matter. You can even level up from 1 to 60 and never complete a single quest if you want. That's the magic of this genre, you can find the way that suits best for you. But looking it realistically, entering the zone and completing all quest in it before going another one seems more like an obsession than reasonable decision. Lets take Ashenvale for instance. You can start questing there at level 18 and highest quests are lvl 30+ in its eastern part, which means a lot of mob grinding to fill the gaps. And there are some quests you can get in Ashenvale but in order to complete them you have to travel to another zones. The quest for killing the mage in Barrens and the quest for wyverns in Stonetalon Mountains comes in my mind. And after level 30 more and more of quests work that way, you don't have a luxury of staying in one zone. There are only a handful of quests for your level before it's time to move and come back later.
Some of those QoL features you listed already were in vanilla. Connected flight paths was added at the end of 2005 (i remember this because i started playing in fall 2005 and they changed it when i was playing my first character) and key ring was there from day one (at least from my day one). I don't know about the rest of them but i can't see why any of them were left out from WoW:Classic since they don't really affect the gameplay.