I would say the other argument that dave2008 is making, is that with his model you can lay an ultra smackdown onto the PCs to the point where they have to use their turn to "scramble" and find a way to not get roasted by the legendary.You are correct.
My point it that I find legendary actions rarely actually change the battlefield. Legendary actions are to weak, IME, to have the impact you suggest. If I have the choice, I prefer 1 impactful off-turn reaction than 3 ineffective legendary actions. Now, these issues can corrected with better design. However, the point is that by design, to maintain CR, each of those LA have to be rather weak.
I will also point to PF2. Monsters in PF2 don't have legendary actions and they make solos threatening by increasing the defense and attack (simply because the monsters are higher level, typical PC level +3-5, no extra actions or reactions). Now, I haven't run PF2, but from everything I have heard, PF2 "solos" work really well. You simply don't need LA to make a monster threaten, no need the right "numbers."
Now, I do like legendary actions and I think they can make a battle more dynamic. I am not suggesting getting rid of legendary actions, only there are other effective ways to make a monster a threat. The big one for me is the correct CR vs PC lvl and # of PCs.
If a PC gets clobbered on round 1 and realizes "if I take that round again I am going to die", than they act a lot differently than if they think they can take another round of punishment.
that's the theory at least. Though I do think this is heavily dependent on the LAs themselves. If we look at the new gold dragon ancient for example, that banish is nasty nasty nasty business, people able to just take a PC out of the round and then drop them anywhere you want in the area is likely far more effective than "simple damage"