Once upon a time, high occupancy vehicle lanes (aka carpool lanes) were pretty simple. If you had some number of people in your vehicle over one, whether a carpool or van or bus, you could use a lane of traffic set aside for you. Nowadays there are all kinds of other people in the carpool lane as well: motorcyclists, people who drive hybrid cars or other clean-air vehicles, and people who pay money in "high-occupancy/toll (HOT)" lanes.
Allowing these other groups of people in HOV lanes is controversial, as is, for that matter, allowing children in carpool lanes to count for purposes of carpooling. And there is good reason for this.
Although it isn't usually stated this way, HOV lanes generally work, when they do, because they directly compensate for what they are intended to encourage.
Carpooling, or taking a bus, takes more time than driving alone. Either way, the vehicle goes out of its way and stops more often to pick up passengers than a single occupancy vehicle would do.
Society benefits from carpooling and transit use, but except for the additional time it takes, in most other ways individuals benefit as well. It's generally cheaper to carpool or take transit than to pay for gas and parking, and because passengers are not busy driving, they can use the time for other things.
But it takes longer. HOV lanes directly compensate for this extra time by reducing the difference in the time needed to travel. Depending on the trip and the mode chosen, it can actually make the trip take less time than driving alone, but even if it isn't that beneficial, it still reduces some of the cost in time. This directly advantages carpooling and transit use in precisely the way that is needed most.
But this is not true for the other possible ways people can use carpool lanes, which trade money for time or cleaner air for time. To the extent that these things make HOV lanes more crowded and less valuable for real HOV travelers, they harm HOV traveling in ways that cannot be easily compensated by the other benefits that they undoubtedly provide.