Remember that 90% of a QOF's assets must be qualified OZ business property, so if the required cash can stay within that framework, you could do it. With a 20% tax rate, I'd think that you would fall short by only holding 10% in cash. On the flip side, you'd also be losing the ability to have some slippage afforded by the 90% rule if you already came up with a specific use for the 10%. You could push this a bit farther by holding up to 5% at the subsidiary entity level, ready for a distribution up in 2026.
Of course, investors were otherwise going to pay the tax currently, so it's not clear why they need the fund to make the cash available to them. It would be somewhat less efficient, but certainly, investors could set aside the money themselves. With a $1M gain, either set aside ANOTHER $200K in anticipation of 2026, OR set aside $200K of the $1M today, and only invest $800K in the fund. Of course, you would now use $40K of your $200K to pay the tax on the $200K that you didn't invest. But the remaining $160K would cover the tax bill on the $800K that was deferred.
Finally, a fund could anticipate BORROWING the $200K in 2026 and making distribution at that time, which would come out tax-free (presuming that the debt was allocated to the investor under the tax rules), and could be used to pay the deferred tax bill.