Would a journal paying money for reviews, with open access and ad-based revenue, work?
Your idea has no chance of success. I'll ignore the part about reviewers being PhD students and postdocs and just look at the publishing model, because that alone is enough to sink the concept.

Ad revenue is not enough to sustain a journal. Just consider: who is willing to pay to advertise in a journal?


You might be able to get some ad revenue in a print journal, but as a whole, print is declining (maybe ~20% of the journal market at this point and dropping), plus with the most lucrative markets (developed countries) almost fully using electronic articles, you're not going to reach much of an audience that advertisers will be interested in.
Plus, if you do print your journal, you have printing costs to pay for.
Even if you go fully electronic, academic journals don't have nearly enough readership to attract advertisers. Just compare how many subscribers you need on a YouTube channel to monetize content (I use YouTube because this is also an advertisement-driven service). YouTube wants one thousand subscribers. Academic articles don't come close to 1,000 readers on average.
And to top it off, not only are you generating no revenue (diamond open access), you want to pay your reviewers. Where are you going to get the money from? You can beg your editorial board members work for free, you can use a free editorial-management system, you can outsource copyediting and typesetting to the authors, you can ignore marketing your journal, you can strongarm your institution to host your journal's webpage for free ... but paying reviewers involves cold hard cash.


The only way this can work is if you manage to secure renewable, external funding. Depending on how much you're willing to skimp on a journal's operating costs, as well as on how many articles your journal gets, you might not need more than a couple of thousand dollars every year. However even this level of funding is not easy to get. There's a reason why diamond open access journals are rare.

tl; dr: you can try, but expect to fail.