That has changed a lot in recent years. Most of the MMO's I've played have a relatively quick advancement with lots of content to burn through and the grind is really mostly at top level for gear. Keep the hard core guys happy with the grind up there. Most F2P games tend to make advancement painful past the first 'set the hook' stage. Yah, both have some element of grind, but where they are on the spectrum is different.
I think the history of MMO level grind is this:
The long history of RPG's centered on levelling chars. The game was levelling, by the time you hit max level, the game was about over.
So when MMORPG's were made, they copied the levelling as being what the game was about, with content made for level after level.
Thing is, after the players finished, say, the level 5-10 area, it was useless to them. It cost a lot to make the content that had very brief player use.
Further, some players could hit the max level fast - not allowing that make it take a really long time for other players. So they had players at max level - and found those players were very iomportant to their revenue to keep them playing, so they needed 'end game' stuff that could last months and years.
They started to realize that the 'levelling content' was very expensive to make for its use by players - that the levelling process was almost superlous if not annoying to many players to have to 'get through', while they had to make the big investments in the end game. I suggested it'd make sense to make an MMO that didn't even have 'levelling', just start chars at max level and make it all about raiding for gear and other advancement.
MMO's haven't quite done that, but as you note, they have greatly 'sped up' the levelling process to get chars to max level - it's almost more of training.
I'm still waiting for an MMO to do what I suggested would make sense for them - between gear, and faction rep, and zone access by killing bosses and more, there's plenty to 'level'.
Another benefit is that it could allow players to play together instead of the 'level 10 wants to play with his max level friend' and awkward 'match the level' features.
Personally, I like the levelling, when it adds to the story and enjoyment, but I think it makes sense for the devs to get rid of it.