Grapple and shove are attacks which can be part of your attack action should not be controversial at all.
Whether every fighter needs more options is an opinion I simply disagree with. If you want someone that slaps on armor and wades into the fight while casting spells or using supernatural abilities you have multiple options with subclasses, barbarians, paladins and so on. If you want maneuvers you can do that. Want to be better at being a defender? Take a cavalier so you can mark with polearm master and/or sentinel to maintain focus on your PC. Want to really make a mess of things? Multiclass. Want to talk endlessly about how awesome your PC is on a spreadsheet? Hexblade.
You don't need complexity for every class. The label we put on classes is artificial anyway, if you didn't know what some classes were called people who aren't familiar with the system wouldn't know the difference. Put another way: if you open up more "tactical complexity" (whatever that means) than we already have to fighters I think you would have to change the structure of combat. That would have massive ripple effects throughout the system.