Override taxonomy term path with Views I need to override by views my hierarchical taxonomy term paths:

www.example.com/[vocabulary name]
www.example.com/[vocabulary name]/term1
www.example.com/[vocabulary name]/term1/term2 
www.example.com/[vocabulary name]/term1/term2/term3


Where

term1 has depth = 0
term2 has depth = 1
term3 has depth = 2


Vocabulary terms: 

+ term1
-- + term2
---- + term3
---- + term3.a
---- + term3.b
-- + term2.a
-- + term2.b

+ term1.a
-- + term2.c
-- + term2.d
-- + term2.e


Paths have been configured by Pathauto

If the path leads to term with depth = 0 I'm using view display "Page".

If the path leads to term with depth = 1 I'm using view display "Page - category".

If the path leads to term with depth = 2 I'm using view display "Page - subcategory".

I tried to use Taxonomy Views Integrator to override the paths by Views, and it's working, but there is one disadvantage in this solution:

If I add a new content and create a new term (with the help of the Simple hierarchical select module ) then I'll be forced to edit this term and select the appropriate view  to override this term path. It might be very time consuming with many terms, so I'm looking for another solution.

How to set a view display for a specific term depth?
I think you are making a little mistake that confuses you. 

TVI does not allow to define a view for the vocabulary itself so the path www.example.com/[vocabulary name] cannot be handled by the module. The vocabulary settings are the default ones for all terms within the vocabulary. These settings can be overriden for each term and can be inherited with the latest version. If you want a specific view for your entire vocabulary, you will have to create it by yourself because no vocabulary page exists by default in Drupal.

If I get your problem described in this post and on drupal.org (https://drupal.org/node/2066015) I can suggest you the following :


Define view1 as a page display and give it the path related to your vocabulary's name
Define view2, view3 dans view4 using any path of your choice, it does not matter as TVI will call them directly
Define view2 as the vocabulary's default view
Define view3 and view4 as term's specific settings if needed


When trying to show a term page, TVI will do the following :


If the term has TVI settings, use it
Else find its first parent having a TVI setting with the "override" option and use it
If no parent is found, use the vocabulary's TVI settings


If I take your drupal.org sample you will have :

Terms

Vocabulary (view2)
T 1 (no settings) 
    T 1.1 (view 3, not inheritable)
        T 1.1.1 (no settings)
    T 1.2 (view 4, inheritable)
        T 1.2.1 (no settings)
    T 1.3 (no settings)
T 2 (no settings) 


Results

T 1 (view 2 from vocabulary)
    T 1.1 (view 3 from itself)
        T 1.1.1 (view 2 from vocabulary)
    T 1.2 (view 4 from itself)
        T 1.2.1 (view 4 from T 1.2)
    T 1.3 (view 2 from vocabulary)
T 2 (view 2 from vocabulary)


I hope this will help you to achieve what you want to do.