What is the point of Feinting from a distance?

Question

This question states that being able to Feint from 30 feet with Grovel is an "unambiguous and clear advantage".

I do not see it. Yes, you can make the target flat-footed from afar, but only against your melee attacks.
So now instead of Striding to the enemy, then Feinting, then Striking, you can switch the first two actions. Where is the clear advantage?

Even if you have a beneficial way of combining a Feint and a Strike, or a Feint and a Stride, it does not help, as the Grovel feat does not modify Feint, but is its own action.

What am I missing?

(this question is not about the Will instead of Perception issue, that is well covered by the answers there)

Answer 1

Better Planning

The primary advantage is that you figure out how well the Feint works before moving up, allowing you to change tactics based on that result.

If you critically fail the Feint, it's probably a good idea to stay at range and avoid the penalty that you've become flat-footed to the target's melee Strikes. Even on a failure you might rather not rush in to attack an enemy if your build depends on something like a rogue's Sneak Attack to deal damage.

Running in and then figuring out the result leaves you adjacent to the target with one less action. You could run away on a critically failed Feint for the same reasons as above, but that's at some serious costs compared to just using Grovel:

• Spends two additional actions to enter then leave melee
• Provokes Attack of Opportunity if they have it, possibly flat-footed because of the Feint

Answer 2

Mobile Finisher

Fencer Swashbucklers are the main users of Feint in my experience, and on level 12 they can take the feat Mobile Finisher. It lets you Stride and Strike in one action, but Feint does not fit in between.

If you have to move, and don't have panache, took Grovel and Mobile Finisher (many ifs), you can spare one action, provided the Feint succeeds.

Cheap Fuel for panache

If there are multiple enemies, with different defenses, you can use Grovel to gain panache on an easy one, while spending it on the Big Bad, against whom you are less likely to succeed with Feint.
However, I would only use this if the Big Bad is off-guard anyway.