This is likely intentional

Can anyone point me to sage advice / RAI clarification / errata?

I was unable to find an official response at the time this question was asked, however Jeremy Crawford recently answered this question directly. See the answer by V2Blast.

I believe you have interpreted the spell correctly, and I believe it is intentionally designed to function in that manner as it follows the same pattern as similar spells.

Compare Zone of Truth:

On a failed save, a creature can’t speak a deliberate lie while in the radius.

To Evard's Black Tentacles:

When a creature enters the affected area for the first time on a turn or starts its turn there, the creature must succeed on a Dexterity saving throw or take 3d6 bludgeoning damage and be restrained by the tentacles until the spell ends.

Or Web:

Each creature that starts its turn in the webs or that enters them during its turn must make a Dexterity saving throw. On a failed save, the creature is restrained as long as it remains in the webs or until it breaks free.

Or Control Water:

When a creature enters the vortex for the first time on a turn or starts its turn there, it must make a Strength saving throw. On a failed save, the creature takes 2d8 bludgeoning damage and is caught in the vortex until the spell ends.

The spells are broadly similar in that:

• Each spell forces a save when a creature enters the affected area, or starts its turn there.
• Each spell specifies an effect the creature will suffer on a failed save.
• Each spell specifies that the condition will last until some other condition is met (spell ends, creature leaves the affected area, creature breaks free, etc...).

Zone of Truth follows the same pattern. It would appear that this is the intended design.

It at most forces one save per turn.

If the creature remains in the greased area, then it might have to save again if it is not already prone. But if it starts its turn in the grease (prone or not) and then exits, it is still difficult terrain. So you want to make sure the enemies will be forced to cross the grease, or at least can't just exit by moving closer to you.

When the grease appears, each creature standing in its area must succeed on a Dexterity saving throw or fall prone. A creature that enters the area or ends its turn there must also succeed on a Dexterity saving throw or fall prone.

So the only moments a creature must make a save are:

1. When the grease appears
2. When the creature enters the area
3. When the creature ends its turn in the area

However, you are interpreting the spell wrong.

It is not a spell meant to keep people prone. It is a battlefield control spell. Need to cover the party retreat? Grease the tunnel behind the last person. Want to make the enemies take longer to get to melee range? Grease between you and them.

Enemies will lose 20ft of movement to cross the greased area in the best scenario (for the enemies).

Also notice it does not use up concentration, and this is a big plus.

There is this video by nerdarchy about using the spell. Except they got it wrong in the first segment. Grease is not flammable. And they got the burning hands spell damage wrong.