There really aren't any immortalized human T cell lines that maintain their cytotoxic properties as well as NK92 cells do. The only one I am aware of is TALL-104, which has been used in clinical trials for a long time now (I don't really know how well they've performed, but those studies are pretty easy to find).
The NK92s have the added bonus that, in addition to having specificity to towards whatever antigen the engineered receptors targets, they also can be activated by a lack of killer-immunoglobulin like receptor (KIR) inhibitory ligands. A really major KIR ligand is MHC-I and tumor cells often evade the immune system by down-regulating this protein (and other inhibitory ligands). Hence, receptor-engineered NK92 potentially have multiple routes towards targeting tumor cells.
As far as "off-the-shelf" T cells, there is some really interesting work being done to use iPSC derived T cells as a source of renewable therapeutic cells. Here's an example of a company working on this: https://notchtx.com/