Undead Monster Classes. (Libris Mortis)

[Zeta Kai]

No natural healing.

That's only for Undead with no Intelligence score, which are unsuitable for PC's anyway, & therefore don't count. There is nothing that says an intelligent undead does not heal on its own.

Also, many Undead have Turn Resistance &/or Fast Healing, which ameliorate many of their weaknesses. Even Constructs aren't as resilient.