It's nice to have it - it gets round the Strength is a rubbish stat issue that 5e has - but it should be instead of attacking, not in addition to!
5e has an issue with Strength being a rubbish stat? Since when? Like so many basic physical things run off of strength in 5e, from jump distances to encumbrance to attacking to overrunning to grappling to resisting grapples and overruns. (albeit overruns are an optional rule). Like dump strength too low, good luck taking basic travelling gear with you.
But I do agree that shove should be an action.
