That is valid. You can show the average (or median if there is a reason to get rid of outliers), but it would be VERY misleading and arguably wrong if you don't show also the uncertainty associated with that mean solution.
However, the whole point of getting the mean of many values is to reduce the uncertainty. Therefore, just plotting a shaded area covering the range over which the original lines were distributed, would be an overestimation of the uncertainty (here I'm assuming that each original line have no uncertainty, which is wrong, but if you have that uncertainty data it can also be included).
A standard way to estimate the uncertainty of the average of many lines (a.k.a Time series) is calculating bootstrap confidence intervals.
Here is an example from a paper I recently submitted:
The mean of all those black lines is the blue line. To expose the spread of the data I decided to show all the original lines. But, if I were to show this to a general audience, I would get rid of the thin black lines and show the mean (blue) and the confidence intervals (pink shades).
Those shades mean that with a 90% confidence the mean should fall within the dark pink shading, and with a 99% confidence within the light pink shading. Giving a sense of how much you can trust the blue line.