Matlab have quite good such capabilities, Octave is more limited (you can't add titles, labels, regression lines or brush away data points, get simple data statistics like sums or std devs like in Matlab, but you can zoom and pan, save to file etc).

Julia seems to launch a Qt-window with plot, so adding some menu bar with zoom and pan shouldn't add too much bloat.

E.g. exploring roots benefits from zooming a lot.

EDIT:

You seem to be able to switch "backend" of Plots to eg. PyPlot for some functionality I didn't know that.

I agree that there's room for improvement here, but I also think that it won't happen in Plots.jl (and if it does, it'll depend on a backend that already provides interactivity). I think it'll be more likely to see something like this plop out of Makie.jl or something built on top of Makie.jl, as that has a lot of primitves for interactivity available already.