OP was looking for a way to get table cardinality for all databases in an instance.  There are many ways to get the result. This post gives you an idea and SQL in which undocumented SP's being called  "sp_MSforeachdb and sp_MSforeachtable".

The above undocumented SP's  iterate through each database and each table of a SQL instance 

SQL:-

SQL
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CREATE TABLE  #TableRowCounts  ([databaseNAme] Varchar(100),[TableName] VARCHAR(128), [RowCount] INT) ; 
 
EXEC sp_MSforeachdb 
@command1 = 'IF not exists(select 1 where ''?'' in (''master'',''model'',''msdb'',''tempdb'')) 
INSERT INTO #TableRowCounts ([databaseNAme],[TableName], [RowCount]) 
EXEC [?].dbo.sp_MSforeachtable @command1 = ''SELECT ''''?'''',''''&'''',count(1) FROM &'',@replacechar = ''&''' 
 
SELECT * FROM #TableRowCounts 
                     
DROP TABLE #TableRowCounts    

Note:-The above query is an expensive query. Please use at your risk

Output-

TableCount-spMSforeachdb&table