I think not giving out any Fate points is a little drastic. Players invest a lot of time and energy into developing their characters and the Fate point mechanic is intended as a failsafe to ensure that they don't have to say bye bye to their characters due to some unlucky rolls.
Having said that, gaining more Fate Points should be a pretty rare occurence and should be awarded for taking risks, risks that make the story better and the game more enjoyable. If your character just makes stupid descisions that are out of character for their PC, then that shouldn't be rewarded. However, if your Space Wolf Assault Marine charges the deamon to buy his colleagues a few seconds to re-deploy but somehow, through cleaver or inspired tactics, manages to slay it or cripple it largely on his own, that might warrant a fate point. Likewise, persuing a series of bold Social tests that might have some possibly catastrophic repercussions for failure might be another example.
As for the more cautious types: there's nothing wrong with those players not getting Fate points. Rather than trusting to Fate/The Emperor/Luck to see them through, they've chosen to put their trust in logic and forethought. Nothing wrong with that.
There are essentially two ways to use Fate points: proactive or reactive. (Ie: get a +10 to a roll is proactive, reroll a roll is reactive.) This means that even the cautious players should be able to find uses for fate points besides Hail Mary's and miraculous recoveries.
Burning fate is not mandatory, by the way. On one instance, our GM gave one of our players a freebie: he'd done something suitable epic and awesome but was struck down. The GM offered to give him a Fate point which he could burn on the spot if he wanted to keep his character. The player choose NOT to burn fate and let their characters die because it was appropriate / cooler that way.
Fate points are intended to make the game more fun by giving the players a little control over the store to oppose the randomness of the die rolls. As long as everybody is having fun and your players still feel a real sense of fear or anxiety when combat starts, you're doing it right.