If you tweaked your back on the lift, I'd lean on the side that you probably didn't have the best form and that caused the problem. Form on this exercise and many others is so important.
I tweaked my back doing heavy bent-over dumbbell rows and like you, stopped doing the exercise for years. I came back to it, but use a lighter weight, watch my tempo (my main focus when doing the exercise) and ensure I control the weight through the entire movement.
Due to the above, I stopped doing deadlifts as well (and I was damn good at them back in the day). I've recently (very recently) come back to the lift and was shocked at the results that I've had in such a short time.
I'd say this exercise is one of the bread and butter ones that anyone should be doing, along with many others (like the squat).
IMHO, anyone can throw heavy weights around, but only a few take the time to ensure their form is correct, they control the weight, and watch their tempo. Try a lighter weight, be ultra-strict with your form, watch your tempo, and control it the whole way through.
I'd also suggest starting with the bent-leg version, rather than the stiff leg version.