Could someone give me an idea when EJBs would NOT be needed
in a web app with a JSP-Servlet frontend and w/some minimal
transaction processing in the back.
EJB is very helpful when the programmer needs to get rid of the risk of Transaction Handling and Threading. Another concept is Reusability.
If the functionality that you are provided in the bean is reuasbale, then also using EJB is good.
If the transaction is minimal with respect to the incoming requests, it is not necessary to use EJB.
But the underlying fact is that in the case of heavy transaction, one can design a system without using EJB. Here the programmer hjas to take the risk of handling the transcation.