Why doesn't simple recovery model support log backup or tail log backup? Lets say there is a crash then we can use the full backup and a tail log backup - because if there was checkpoint then data would already be written to the database data file and flushed from the transaction log. Where as if there was no checkpoint yet then logs will still be there in the transaction log file. So is recovery possible in this recovery model?
The logs written between the FULL backups and the crash will be overwritten at some point
They are not saved with BACKUP LOG.

My bold describing Simple


  Every transaction is still written to the transaction log, but once
  the transaction is complete and the data has been written to the data
  file the space that was used in the transaction log file is now
  re-usable by new transactions.


From SQL Server docs


  Automatically reclaims log space to keep space requirements small,
  essentially eliminating the need to manage the transaction log space.


In theory, a crash happening just after a full backup that has just a few transactions might work, if the LSNs match.

In practice, this is almost never guaranted to happen so for consistency (and false hope) better to disallow this in simple recovery model