The Floyd Rose tremolo arm (whammy bar) design is renowned for staying in tune, even after the most extreme dive bombs.
Unlike other guitar designs the strings are trapped at the nut, not free to move over it. This engineering design does have advantages for tuning stability.
But are they that great? Do you need one?
Well they have pros and cons
The advantage of a Floyd Rose
For studio work you can get as close as 1 cent in tune on every string - and it will probably remain that well in tune for not just the session but days! Only moving the instrument into an environment with a different temperature will put it out. Even then, the different strings will be relatively in pitch, even though they lose concert pitch. Good enough for Rock & Roll (as they say!).
This very stable tuning makes a Floyd Rose the best tremolo arm you can get.
The disadvantages of a Floyd Rose
1. The Floyd Rose is a hassle to string.
2. The whole instrument goes out of tune when a string breaks.
Won't recover quickly if a string breaks at a gig - but then you should have a backup guitar even (if you don't have a Floyd Rose).
You need tools, well an Allen key, to change a string. That's easy to lose, hard to find!
Conclusion - do I need a Floyd Rose
Arguably you only need a Floyd Rose if your playing style requires a tremolo arm - Rock and shred styles for example.
Though the stable tuning is a reason in itself.
Tip. I have my luthier lock my arm off, a very simple operation, so you can only go down in pitch.