Yes, very clearly a virus with a higher R value causes the percentage of the population required for herd immunity to go up. This is how science works.
The R value for the original COVID was around 2.5; the R value for the Delta variant is between 5 to 9.
Seeing that these hospital medical systems have thousands of employees... and only 10 or so people in the crowd are actually employees.... these medical systems now know exactly who to fire.