All DOS mouse drivers were TSRs. The driver would hook INT 33h (which is the mouse driver "API" entrypoint) and whatever IRQ (ie. 4 or 12) that the actual hardware used. The IRQ handler would then update the driver's internal state according to data received from the mouse and if enabled draw the mouse cursor into frame buffer and/or call registered user event function (which runs in the interrupt context).
There isn't anything inherently unreliable with TSRs; DOS even provided interrupts for this specific operation (although some malware would not use them).
I think (although not entirely sure) that some mouse drivers were, for example, TSRs.
The problem is that there was a wide range of purposes and implementations, including malware, so the argument is similar to "BTC is mostly used for dirty money, so BTC is inherently criminal".