I'm thinking there's probably nothing to worry about, but it seems like it could make the game a lot more linear as there will most likely only be a couple of set paths up each mountain?
The mountains could be really annoying if you're just wandering around and you come to the base of the mountain and realise there is no path up it or around it unless you walk for ages to find the set path. I'm fairly confident they will have planned on this and it won't be as bad as the mountains in Oblivion as these mountains are presumably something they really focused on designing.

There will be a ton of content tied to the mountains, they won't be mundane. Plenty of caves/POI's/word walls/loot/etc. We'll be able to traverse them with paths and caves that lead up and through them. I'm sure they spent a lot of time designing them since there's a lot.

Here’s to hoping that any mountain the player can’t climb over has a cave or something to go through instead.

Yeah I guess caves would be a good option, I'm actually really looking forward to exploring all the caves and dungeons because they seem to be looking much more diverse and well designed (artwise and gameplay wise), whereas in Oblivion you've seen one cave you've pretty much seen them all.
So yeah I'll be happy if they choose this option to traverse through mountains.

A big step up from Morrowind's linear valleys.

Definitely Kratos!

I really think the mountains will be climbable even without using a set path.... it might look ugly but I am sure its possible..... people are scared of and elder scrolls game being to linear? come on people!

The difference is in morrowind you were not welded to the path. With jump being neutered, levitate staying away you are stuck to the paths in rigid terrain which does make it more linear. Whether that is good or bad is up to you.