There is some truth in what you say. Though steam engines still power most of the power grid (especially in the "developed world") their capital costs are indeed too high to be economically competitive.
However, there are also some errors.
In 02022 24% of total US electrical power generation capacity was combined-cycle gas turbines (CCGT), https://www.eia.gov/todayinenergy/detail.php?id=54539 which run the exhaust from a gas turbine through a boiler to run a steam turbine, thus increasing the efficiency by 50–60%. So in fact a lot of gas turbines are installed together with a comparable-capacity steam turbine, even today.
Syngas is not a technology that "just doesn't work". It's been in wide use for over two centuries, though its use declined precipitously in the 20th century with the advent of those natural-gas pipeline networks. The efficiency of the process has improved by an order of magnitude since the old gasworks you see the ruins of in many industrial cities. As you say, though, that isn't enough to make IGCC plants economically competitive.
The thing that makes steam engines economically uncompetitive today is renewable energy. Specifically, the precipitous drop in the price of solar power plants, especially PV modules, which are down to €0.10 per peak watt except in the US, about 15% of their cost ten years ago. This combines with rapidly dropping prices for batteries and for power electronics to undercut even the capex of thermal power generation rather badly, even (as you say) if the heat was free, whereas typically the fuel is actually about half the cost. I don't really understand what the prospects are for dramatically cheaper steam turbines, but given that the technology is over a century old, it seems likely that its cost will continue to improve only slowly.