There is an inconsistency in the PHB about the spell Etherealness. The spell description states that you cannot use it to travel to other planes:
When the spell ends, you immediately return to the plane you originated from in the spot you currently occupy. (PHB p 238)
While later in the Planar Travel section the PHB suggests that you could use Etherealness to travel from the Border Ethereal to the Deep Ethereal, and from there to another (material/inner) plane.
Etherealness allows adventurers to enter the Ethereal Plane and travel from there to any of the planes it touches- the Shadowfell, the Feywild, or the Elemental Planes. (PHB p 301)
However, even if the PHB's later description of the spell is the intended ruling, isn't Etherealness too short a spell to make such a journey? Its duration is 8 hours, and the DMG states travel times in the Deep Ethereal:
A trip between planes through the Deep Ethereal takes 1d10 x 10 hours, regardless of the origin and destination. (DMG p 49)
This would be at minimum 10 hours, which is more than 8. I suppose an Extended Spell Sorcerer could manage it 1 in 10 times though…
Best Answer
You are right. This is an oversight.
8 hours is not long enough to travel to a bordering plane through the deep ethereal, not to mention the journey to get there from the border ethereal.
Even if you could reach the other plane, you would be sent back to the plane you started on as soon as the spell ended. You would have to cast etherealness again to tether you to the new plane and then return to that plane after the first spell ended.
As such, the etherealness spell is not an effective means of planar travel, like the section in the Player's Handbook suggests.
Why the rules then?
Perhaps it is easier to attune a forked, metal rod to the Ethereal Plane for the purposes of plane shift since you can get there via etherealness. Then you can travel to the Ethereal Plane long enough to make it to the inner planes.