Taking away the ability to shove first nerfs the feat, and makes the sword & board style less attractive. The advantage still has to be earned via an opposed roll. If you nerf it, those who care about being effective will choose PAM & GWM instead. Why would you want to encourage everyone to make the same choice?
If you take the bonus action shield shove first, since that is dependant on taking the Attack action this turn, then you have locked yourself into the Attack action. If something happens after the shove that would prevent you from taking the Attack action, or would leave you in a situation where the Attack action is no longer useful, tough! Them's the breaks!
I'm going to attack/shove the baddies. Since the BBEG standing on the edge of a cliff I'll try to shove him off the edge. I'll probably fail, but I'll then attack him twice. But in the unlikely event I succeed I'll move to his wizard henchman and try to kill him. Wow, I did it! The BBEG falls to his death (or did he?) so I turn to the wizard. As it turns out, the wizard was low on HP and had Readied an action to teleport home if the BBEG was defeated. As I turn to the wizard, he disappears. There is no-one in range that I can attack, so I'd rather Cast a Spell instead. Sucks to be me though, because taking the bonus action shield shove locked me into that Attack action, like it or not.
See! It's easy to adjudicate.
The only thing that's unbalanced is the guy who got hit by the shield!