While I agree that generally speaking your DM ought to let you take sensible actions (like attempting to disarm or take cover), the viability of those actions as regular combat options does to an extent depend on feats. If it takes my action (or at least one of my attacks) to knock someone prone, it may not be worth it, but if I can do it as a bonus action (which makes sense for an experienced shield wielder), it becomes a great tactic.
Feats also allow you to do things that would normally be impossible. If a player didn't have an ability that made him or her able to do it, I wouldn't allow them to duck behind their shield as a reaction to avoid a dragon's fire breath, because the rules already assume that player is doing everything they can to avoid the fire breath. Just like I wouldn't give advantage on an attack roll if the player said "I aim for the head," because a character's skill at aiming is factored into their attack bonus.
That said, fighters are able to do just fine in a game without feats. Remember, grappling and shoving only take up one of your several attacks, so use those liberally to gain an advantage! If you grapple + prone a foe, they stay proned until they can escape the grapple (as an action!), and many foes aren't proficient in Athletics - a great way for Fighters to get some battlefield control in!
Feats also allow you to do things that would normally be impossible. If a player didn't have an ability that made him or her able to do it, I wouldn't allow them to duck behind their shield as a reaction to avoid a dragon's fire breath, because the rules already assume that player is doing everything they can to avoid the fire breath. Just like I wouldn't give advantage on an attack roll if the player said "I aim for the head," because a character's skill at aiming is factored into their attack bonus.
That said, fighters are able to do just fine in a game without feats. Remember, grappling and shoving only take up one of your several attacks, so use those liberally to gain an advantage! If you grapple + prone a foe, they stay proned until they can escape the grapple (as an action!), and many foes aren't proficient in Athletics - a great way for Fighters to get some battlefield control in!