If Phantasmal Force had a save every round like many spells, then yes, I would think that it could be mobile and used to distract a dragon. But as written, forcing a dragon to use up an action to get the equivalent of a save versus a second level spell is overpowered compared to every other second level spell in the book.
In our game, we are playing that if you are taking an action and directly, physically, interacting with the illusion, then you are very likely going to get a saving throw to notice it is fake. This is the "take an action to investigate" part of the spell description. In the end, it basically ends up costing an action to get the save, which is roughly how the save-ends type spells work at this level (ie. hold person wastes the targets round and then gives a save at the end of it, same with Tasha's). In some cases, the creature can just ignore the effect, so it is a bit worse, but PF gets added flexibility and targets a different save to make up for it.