The short answer is that mongrel mage simply isn’t compatible with any of the archetypes that grant modified bloodlines. The line in the archetype is largely redundant since to get any of the modified bloodlines you must take an archetype for them to start with, including Wildblood, and all such archetypes modify the Bloodline class feature. It was added as a future proofing incase a later archetype were ever written that was somehow capable of being taken alongside mongrel mage and granted a modified bloodline. Wildblood bloodlines are unfortunately granted by an archetype as well, a rather poor design choice in my opinion, since they read and function no different than sub-schools or sub-domains...
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Because wildblooded and mongrel mage are both archetypes that modify bloodline powers they are not compatible.
Although wildblooded was written before the language of “modifies class feature X” was standardized, there is a FAQ confirming that it does modify bloodline powers.
The animal companion from the Sylvan bloodline would be problematic with Mongrel Mage, since it replaces both the arcana and the 1st-level power. A Mongrel Mage doesn't gain the arcana unless they spend mongrel reservoir points, but they have the 1st-level power all the time.
Maybe they didn't want to address that problem and potential similar future problems.