Aren't they normally considered to be overwritten/replaced?
I wonder if these bonus skill points can't be re-phrased as a certain number of bonus Skill Focus feats, and then a note in the multi-classing rules to say that if you multi-class into a new class that would have more, then you immediately gain additional bonus Skill Focus feats equal to the difference.
It's one of the less thought out rules in 3.5, IMO, together with max hp at first level.
Sure, it makes sense to give starting characters some kind of boost to make sure they're not totally useless (starting out with 1hp and/or 1 skill point isn't much fun)
However, it immediately brings up the power decision for multiclassing:
If you're building a Multiclass character that depends on skills, take your first level in the class with the highest number of skillpoints/lvl, because you'll be getting the most out of it at that level.
If you're building a Multiclass fighter character, take the class with the highest HD at first level, because those hp will be maxed.
Then think about templated PC's, where their "first level" is in something like "being a Half Dragon". Do they lose out on the x4 (or x6) multiplier?
If not, why not?

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.