I would argue that it fails horribly in that aspect, for several reasons.But that's the thing. It was made as a way along with raise dead/resurrection, for players to keep their characters continuing on..
First, you need a 12th level wizard for reincarnation or a 14th level priest for reincarnate. But you only need a 9th level priest to gain access to raise dead. Far easier to find a priest to cast raise dead.
Second, in many cases the reincarnated character does not gain a PC/class-able character. Using the wizard version (reincarnation), there is a 47% chance the player will come back as an evil, non-classed race (ogre, orc, bugbear, goblin, etc). Going BTB, these characters cannot have a class. That means no xp, no leveling, etc. The new PC will essentially be a monster.
Third, the priest spell reincarnate is even worse. There is a 50% chance the PC is coming back as an animal (badger, stag, etc), which again means no class, no leveling, etc. Worse yet, the newly incarnated PC is at best a pet. It cannot wear armor, wield weapons, and so on - as opposed to a bugbear, orc, or even a goblin. There's an additional 14% chance the new character is a forest being such as a faun or a pixie. Again, not an adventuring race or able to have a class. There is an overall 64% chance the character is not coming back as a character who can have a class and therefore gain levels.
Fourth, while the reincarnated PC can gain his original form and class via a wish, the wish itself - by its very definition - renders the reincarnate/reincarnation spell(s) irrelevant and unnecessary.
So it doesn't really allow a character to "continue on". It allows the player to play a monster or an animal. They can forget casting spells, wielding weapons, using weapons, using magic items, gaining levels, etc, etc. They forgo everything that makes a PC a PC. Which is why I think it makes far more sense to simply create a table of the various PC races along with some races the DM deems acceptable to use as PC classes, and simply allow the spirit of the reincarnate being to determine class and alignment. That makes more logical sense both in-game and mechanics-wise than anything else.