SSMS 2016 forced connection
@sqlband I can confirm that this a bug ( or feature) of SSMS 2016.

I was able to reproduce this in SSMS version Microsoft SQL Server Management Studio    13.0.16106.4.

USE [master]
GO

CREATE LOGIN [ssmsspeed] WITH PASSWORD=N'ssmsspeed', DEFAULT_DATABASE=[WideWorldImporters], DEFAULT_LANGUAGE=[us_english], CHECK_EXPIRATION=OFF, CHECK_POLICY=OFF
GO
USE [WideWorldImporters]
GO
CREATE USER [ssmsspeed] FOR LOGIN [ssmsspeed]
GO
USE [WideWorldImporters]
GO
ALTER ROLE [db_owner] ADD MEMBER [ssmsspeed]
GO


Now connecting to SSMS using ssmsspeed login. When I expand the database node it takes about 10 seconds to expand as explained by OP. I can see this in my error log and in my security audit file.


  Message Login failed for user 'ssmsspeed'. Reason: Failed to open the
  explicitly specified database 'AdventureWorks2014'. [CLIENT: ]
  
  Error: 18456, Severity: 14, State: 38.


If I list my user databases order by name AdventureWorks2014 is the first one.


AdventureWorks2014 
GMODBA
hacked
test
Warehouse
WideWorldImporters


I also tested this by making Master database as Default_database but same result.

USE [master]
GO

CREATE LOGIN [ssmsspeed1] WITH PASSWORD=N'ssmsspeed1', DEFAULT_DATABASE=[Master], DEFAULT_LANGUAGE=[us_english], CHECK_EXPIRATION=OFF, CHECK_POLICY=OFF
GO
USE [WideWorldImporters]
GO
CREATE USER [ssmsspeed1] FOR LOGIN [ssmsspeed1]
GO
USE [WideWorldImporters]
GO
ALTER ROLE [db_owner] ADD MEMBER [ssmsspeed1]
GO


When I do the same test in Microsoft SQL Server Management Studio  12.0.4100.1 I cannot reproduce this. Expanding database node is instantaneous and no login fail message in error log.