At my prior job, on the wknds we were running the following on Saturday night:

Stop Logshipping;

Set Recovery mode to Simple;

Reindex;

Update Stats for some indexes;

Flip Recovery mode to Full;

Backup;

Copy and Restore on Secondary;

Start applying Logs on Secondary.

Everybody recognized the performance issues when we missed week or two without reindexing, so flipping between Recovery Modes and Restoring to the Secondary of the Backup was always a priority. Few times when we forgot to set Recovery to simple on weekend ( 3AM Sunday, tran log dump grew to 70GB-try to copy it to the Secondary!)