Can fighter use Commander’s strike when he only has one attack?

Question is about Battle Master maneuver. From PHB (74):

Commander’s Strike. When you take the Attack action on your turn, you can forgo one of your attacks and use a bonus action to direct one of your companions to strike. When you do so, choose a friendly creature who can see or hear you and expend one superiority die. That creature can immediately use its reaction to make one weapon attack, adding the superiority die to the attack’s damage roll.

Archetype is acquired at 3rd level and fighter, in general, will have only one attack. If attack is used for maneuver, would it be an attack at all?

From attack description, PHB(192):

The most common action to take in combat is the Attack action, whether you are swinging a sword, firing an arrow from a bow, or brawling with your fists. With this action, you make one melee or ranged attack.

But in this case fighter will not, say, swing his sword. So it doesn’t fit with description.

If a fighter has only one attack, can he forgo it to use commander’s strike?

What are the ramifications of making the Battle Master fighter’s Commander’s Strike maneuver no longer require the Attack action?

The Battle Master fighter’s Commander’s Strike maneuver (PHB, p. 74) states:

When you take the Attack action on your turn, you can forgo one of your attacks and use a bonus action to direct one of your companions to strike. When you do so, choose a friendly creature who can see or hear you and expend one superiority die. That creature can immediately use its reaction to make one weapon attack, adding the superiority die to the attack’s damage roll.

However it is currently the only maneuver that actually requires you to take the Attack action. I found this odd, and the rare times that this fact came up, I simply ignored it, allowing it to be used with any sort of attack. I have thus made the following changes as a house rule:

When you make an attack on your turn, you can forgo the attack and use a bonus action to direct one of your companions to strike […]

It would still be limited to one use per turn, as you only have one bonus action on any given turn, but perhaps there is some issue that results from this which I haven’t noticed. What are the ramifications of this change?

Mount & commander’s strike

Here’s the scenario: A player with 5 levels in Paladin and 5 levels in fighter (Battlemaster).

The player casts “Find Steed” and summons a warhorse and mounts it. During their turn in combat the player attacks and then uses their battle maneuver “commander’s strike” and chooses their warhorse. Would the battle maneuver allow the warhorse to use its reaction to make an attack?

If the answer to the first question is a ‘yes’ then would the warhorse also be able to use its Trampling Charge trait after its attack? Assuming of course that it moved 20 feet in a straight line.