For enough money, they might. If I'm not mistaken, the "community treasury" has 50% of all ENS. This comes to 0.5 * 100MM = 50MM ENS. At current exchange rates (assuming no slippage), that comes to $17.92 * 50,000,000 = $896,000,000.

I'm assuming ICANN approved all this gTLD nonsense because they like the money. This naturally raises the question: how much money would they need to approve this? And is it more or less than $0.9 billion dollars?

Money isn't the issue. If it were, other parties (like the various claimants to .app) would have b̶r̶i̶b̶e̶d̶ convinced ICANN to favor their applications by now. The real issue is simply that ICANN is a highly bureaucratic organization; they don't do anything quickly. They only published a report on the outcome of the 2012 gTLD offering last year.

There are private TLDs like .google that don't use the registry/registrar model, right?

They do, actually. Charleston Road Registry (an entity owned by Google which also operates other TLDs like .APP, .DOG, and .FOO) is the registry; Google is the sole registrar. As far as I'm aware, all of the private TLDs operate on some variant of this model.

But it goes beyond just having those two distinct entities -- any ICANN TLD is expected to follow a set of operating policies (e.g. domain registration, renewal, transfer, expiry, and redemption; dispute resolution; WHOIS verification... etc) which is fundamentally incompatible with ENS.