Shadow Priests are an example of a successful class in WoW. They combine good DPS with solid utility and are in high demand in raids. They heal and regen their group while they DPS. They are often regarded enviously by paladins who wish to be fluid hybrids, to heal and melee in the same fight. So what makes the shadow priests successful? In my view, there are three significant reasons: minimal time costs; one scaling mechanism; and the fact that the sum of their parts is greater than 100%.
Minimal Time Costs
A Shadow Priest's utility comes from the spells Vampiric Embrace (which provides health to the party) and Vampiric Touch (which provides mana to the party). A Shadow Priest spends 1.5s every minute casting VE, and 6s casting VT. The rest of the time is spent dealing damage. Further, VT is actually good DPS (eyeballing it, it looks better than Mindflay). So a Shadow Priest actually spends 97.5% of her time doing damage, all the while contributing health and mana regen to her party. This means that the Shadow Priest can actually come extremely close to her maximum possibly DPS (disregarding threat).
In contrast, if a paladin casts a heal, she reduces her DPS by the equivalent amount. If she casts only a single Flash of Light every 10s, her DPS drops to 85% of her maximum. If she swings her weapon, she reduces her healing throughput, just though time costs.
One Scaling Factor
A Shadow Priest only has one scaling factor for both her damage and utility: spell power. VE and VT scale with spell power. That means that a Shadow Priest only has to collect one stat in order to maximize both her utility and her damage.
In contrast, each side of the paladin's nature has a different scaling factor. DPS scales with Attack Power, threat scales with Spell Power, while healing scales with Healing Power. All scale with Spell Power, but damage and healing does so poorly. Having multiple different scaling factors encourages the paladin to choose one and specialize, ignoring the other.
Sum of the Parts is Greater than 100%
The deep truth of hybrids is that to be less than 100% of any pure dimension (tank, healing, dps) is a huge drawback. The other side of a hybrid must contribute more to make up for that fact. A hybrid that is 50% of a dps and 50% of a healer is simply not good enough. In my opinion, the sum of the two sides must be closer to 150% to even be considered for a raid.
However, this looks unbalanced, but it really isn't. The only two successful fluid hybrids in WoW are Shadow Priests and Feral Druids. I would class Shadow Priests as 90% dps and 60% utility, and Feral Druids as 90% tanks and 60% DPS.
The hard part here, though, is keeping the class from becoming 150% in one aspect. For example, if the paladin was a 75%/75% dps/healer hybrid, what would stop a paladin from not dpsing, and becoming a pure 150% healer?
Minimal time costs, one scaling factor, and the fact that the sum of the parts is greater than 100% are the reasons that the Shadow Priest is a viable hybrid. You can do the same exercise for Feral Druids, and see that all three reasons apply to them as well.
In my opinion, time costs are most important barrier to hybrid viability. You always have the choice between casting a heal or swinging your weapon. If one option is always a better choice for a particular spec, you don't have a fluid hybrid.
If Paladins are ever to become a fluid hybrid, I think that they will need to be changed such that they follow these three rules.