There's a better case for the stock being priced at $25/share with 5 billion shares outstanding than at $7.50 with 17 billion shares outstanding
No, because a 17:5 reverse split in the latter case makes them identical. If there's a good case for one, it's an equally good case for the other.
None of this post actually answers why $7.50 per share is less likely than $25 per share. All FHFA has to do is the 17:5 reverse split first, then the offering really is at $25 per share (but $7.50 per share on a split-adjusted basis).
In fact, at $7.50 per share the new buyers get a larger percentage of the companies, so that price is more attractive to them than $25 per share. They are the ones that have to be enticed to the table, and will want the offering price to be as low as they can make it.
The only counterbalancing force is the warrants. Treasury, with their 79.9% stake, is the only party with power that has a reason to keep the share price high.
But once Treasury exercises the warrants, there will be 9B shares outstanding, and that's without any junior conversion or new share sales at all! The total share count at the end is going to easily exceed 13B no matter how you slice it. Then, by your own argument, there will have to be a reverse split because that's too many shares for one company to have.
The commons trade at around $3 right now, and the prefs are 35-40% of par. There's a reason for this: the market still perceives possible downside for both classes. Don't get caught up in the idea that the commons (or even the prefs) can't lose from here.