I think this is one of those issues that are subjective, and will prove to be preferable, but:
In terms of readability, I would argue that it is explicitly ONLY when necessary. Quite often, SQL statements are quite complex, without having to read a lot of unnecessary text.
I think that
SELECT TOP 1000 [StoreNumber] ,[Address1] ,[Address2] ,[City] ,[St] ,[Zip] ,[ZipSuffix] ,[LocationType] ,[LocationSubType] ,[Corp] ,[Division] ,[ZoneNumber] ,[DistrictNumber] ,[StateNumber] FROM [CommonData].[dbo].[vw_StoreData]
is a lot more readable than
SELECT TOP 1000 [CommonData].[dbo].[vw_StoreData].[StoreNumber] ,[CommonData].[dbo].[vw_StoreData].[[Address1] ,[CommonData].[dbo].[vw_StoreData].[[Address2] ,[CommonData].[dbo].[vw_StoreData].[[City] ,[CommonData].[dbo].[vw_StoreData].[[St] ,[CommonData].[dbo].[vw_StoreData].[[Zip] ,[CommonData].[dbo].[vw_StoreData].[[ZipSuffix] ,[CommonData].[dbo].[vw_StoreData].[[LocationType] ,[CommonData].[dbo].[vw_StoreData].[[LocationSubType] ,[CommonData].[dbo].[vw_StoreData].[[Corp] ,[CommonData].[dbo].[vw_StoreData].[[Division] ,[CommonData].[dbo].[vw_StoreData].[[ZoneNumber] ,[CommonData].[dbo].[vw_StoreData].[[DistrictNumber] ,[CommonData].[dbo].[vw_StoreData].[[StateNumber] FROM [CommonData].[dbo].[vw_StoreData]
(It gets worse when you start joining tables, and even worse if you join tables in different databases.)
I can see where you can argue that the second is more readable if you need to know exactly which database, schema, and table a particular field appears in, looking only at the request.
But in SQL Server, for example, you can open this query in the designer and see it in a much more convenient graphical representation.
IMHO, the only time I will use the full syntax, if necessary , when crossing the borders of a table / database / schema, or if you have two tables with the same field name.
Example:
SELECT TOP 1000 [CommonData].[dbo].[vw_StoreData].[StoreNumber] ,[Address1] ,[Address2] ,[City] ,[St] ,[Zip] ,[ZipSuffix] ,[LocationType] ,[LocationSubType] ,[Corp] ,[Division] ,[ZoneNumber] ,[DistrictNumber] ,[StateNumber] FROM [CommonData].[dbo].[vw_StoreData] Inner Join [CommonData].[dbo].[vw_StorePhones] ON [CommonData].[dbo].[vw_StorePhones].[StoreNumber] = [CommonData].[dbo].[vw_StoreData].[StoreNumber]
And even so, I would use Table Aliases to shorten it and make it more readable.
All this suggests that in the real world you are likely to find yourself in a company that has already decided on a standard format, and you will need to encode in accordance with the standard of the company.