|Image Source: http://metricshr.net/shop/benefits-calculator/|
These resources are often a "meta-resource", meaning that these points are player assets, but do not represent something that the character can control or call upon. The forces of Fate, twists of Luck, the benefits of experience; all of these can manifest as benefits within game. Likewise, these benefits can be completely abstract, having no direct character stat that drives them; a true "meta" resource. It's not like a character is thinking "time to burn an XP to make this easier", that is happening outside on the level of the players and GM.
Other times the resource can be tied to a character statistic or ability that can be improved on by the player. Willpower in the World of Darkness is a good examples of this. Quite the opposite of the meta-resources Willpower is a character trait that the characters themselves can be thought of as using. They are expending mental effort, focus, and determination to improve their chance of success (or do something special), and are conversely weakening themselves against their potential to give in to certain kinds of actions (succumbing to their vices or natures). In addition to the mechanical benefit there is a role-play benefit as it helps to inform the character's action deeper into play.
As I discussed previously that in some games these benefits come to the players as a direct result, and balance, of various mechanics of GM Fiat. In FATE character get more FATE points when their Aspects are triggered against them. in Star Wars Edge of the Empire, the players gain a light side force point when the GM spends a dark side point (and the reverse is also true). Numenera sends XPs to the players when the GM uses an Intrusion. All of these (and plenty more) provide a give and take during the session, as the fortunes of the characters wax and wane. Some of these systems allow for players to spend available points to reject the offered point, and the negative effect that accompanies it; more control for the players, and more ways to balance the GM's power to touch the story directly.
Other systems have their own ways for players/characters to gain or regain points. Willpower can be gained by giving in to a character's baser nature, or by upholding their higher ideals, both of which can pose difficulty to the player, the former often comes back to bite them, while the later usually means taking the "high road" which is often harder.
I've played, and run, a lot of RPGs in the years I have been a Gamer. I've read even more, some I never got the chance to play, others just never got past the point of reading for various reasons. regardless I have found that game systems that utilize benefit type resources offer a style of play that appeals to me. There is some control over failure, there is some measure of means to ensure success, there is some way to say "no" to the GM. I may not have missed it back when I played games that didn't use them, but I find that now that I have I miss them when I play games that do not.
This isn't a bad thing, not all games should have a benefit kind of system, it works better for some games than others and for some kinds of games. A horror game wouldn't work nearly as well if the players could re-roll a failed check or say "no" to being ambushed by zombies. Conversely a superhero game loses something when the players have no way to double down in the final act, to draw deep on their reserves and make that double fist strike hit, or MacGuyver a solution to the villains devious trap.
In the end benefit mechanics are going to be something that people will have to decide for themselves if they like or not, and a game designer is going to have to decide if they belong or not (and what kinds of benefits they should bestow), but I think that they are a tool that is generally a positive addition to the gamer's toolbox.