Ok, let me explain in simple words. No, you cannot reduce it to „just searching the job you want“. Information asymmetry means that:
1. not everyone is aware of all the opportunities available on the market, e.g. when skillset is matching different type of the job people have not considered
2. …or where to find them, because there are many job boards and not everything even lands on them
3. …or that they should look for them at certain moment of time
Push ads address all 3 problems, reaching e.g. those who are employed and not actively looking, but open to change. If a man gets that ad, but a woman not, it means that that man spent zero time to find that opportunity and woman may not even find it in active search. Effectively they pay different costs for getting a better job.