If we assume that a posting costs $1 in either direction, the $100 cost to a company of any significant size of posting a single job to 100 sites is pretty negligible.
On the other hand, to someone who has no job, paying $100 to apply to 100 jobs might be pretty harsh—and there isn't the remotest guarantee that this would actually result in getting contacted, let alone getting a job.
Going one step further, paying that kind of money to apply also means you'd be expected to have a credit card or something similar. At the very least a bank account. And someone who's got excellent qualifications, but had a medical disaster cost them their previous job and home, and has been spending time on the streets, is going to have a very hard time maintaining a bank account or obtaining a credit card without an income.
Basically, any time you make a proposal to "solve" the problems with hiring/job searching, you need to ask yourself, "Is this going to nontrivially exacerbate existing class divides?" If the answer is "yes", that's a) probably why it hasn't been done already, and b) why anyone with any compassion (or understanding of the long-term consequences of inequality in society) should reject such a solution.