Am I wrong saying that immediatelly after the full backup, the transaction log is useless?
Yes, that is quite wrong.
The transaction log would still be needed to recover to a point-in-time after the full backup. If you never need to recover to point in time / you can recover only to diff backups and still be good, then you don't need to do log backups and should stop doing them.
Command DBCC SHRINKFILE(2, <size_in_mb>) can be used to shrink a log file, but you don't want to shrink below what you actually need in the log file. Otherwise SQL will just grow the log again, and that is huge overhead compared to just leaving the space allocated to the log there.
SQL DBA,SQL Server MVP(07, 08, 09) Prosecutor James Blackburn, in closing argument in the Fatal Vision murders trial: "If in the future, you should cry a tear, cry one for them [the murder victims]. If in the future, you should say a prayer, say one for them. And if in the future, you should light a candle, light one for them."