It makes no sense for the US. Sovreign wealth funds make a lot of sense because they can take surplus income from tax revenues and invest it in a productive country like the US. Or they can be used even out income from a limited resource so that one generation doesn't get all of the oil revenue while future generations have to make up the deficit in revenue once that literally dries up.
But the US is in a very different position because we have such a large and diverse economy that if we need dividends from successful business enterprises, we can simply tax our domestic businesses and citizens.
Look at two scenarios.
1A) The government gives you $200 tax break thanks to tariff revenues.
2A) You put that $200 into an S&P500 fund.
3A) You get taxed $20 later to pay for a new aircraft carrier.
1B) The government puts $200 of tarrif money into an S&P 500 fund.
2B) The government takes $20 out of the S&P 500 fund to pay for their new aircraft carrier.
Scenario A is actually the traditionally conservative argument: the state should give people any left over money and the people should decide how to spend/invest it.
The problem with Scenario B (The fund) is it's practically engineered to funnel money to the wealthy. IF the government gives me $200, I might spend it on a SPY etf, or I might go down to my local small business and buy $200 in books and "invest" in their business by boosting their sales.
The only organizations that a US Wealth Fund would invest in are going to be public traded large corporations who probably don't even need any higher valuations and will only serve to boost the stock portfolios of the upper class. Aka they're going to boost the likes of Meta, Microsoft, Amazon, Tesla and Apple.... hmmm, who was it at the inauguration? Coincidence? The CEOs will see their stock options blossom. The small business that could use local cash being spent will get nothing.
Why would a country like Singapore though have a wealth fund? Because as a micro-nation they have a lot of cash from their ports coming in but not a lot of opportunities to invest domestically. The US can just tax Google profits. Singapore can't just tap Google profits for tax revenue.