It isn't really suitable to replace the steam engine; its inventor did hope it would but I think it had ample opportunity to do that OTL if it were going to.
The characteristics of the engine made it more a precursor of applications we'd use small electric motors for today.
I guess I have a problem with wanking a technology that I know was available to clever people for the better part of a century before other types of engines could be said to preempt it unfairly--so, we cannot say they did that. The world had Stirlings available long before electric motors for fixed applications, or the more familiar kinds of IC engine in both Otto and Diesel types made their first significant appearances.
Specific characteristics that I think made it less attractive
1) a limited band of optimal efficiency power output: Piston type steam engines deliver plenty of torque from a standing stop as do some kinds of electric motors; like IC type engines, the Stirling is not much good at a standing stop and needs to get revved up before it can efficiently put out power. For a road vehicle this corresponds to a certain range of speeds; you'd need a gearshift to enable the optimal RPM band;
2) Limited power output; heat must flow into the hot intake cylinders and out the heat dumping cylinders; with steam engines and IC engines these flows are of the working gas itself, with a Stirling the working gas is contained and heat must flow through solid surfaces, which limits power.
Now I've seen it suggested that actually the engine ought to work wonderfully well for a boat or ship, since the efflux of waste heat would be well accomplished dumping it into water that would very efficiently cool the output surfaces.
But again I have to ask--given that the device was well developed by its inventors and it would take until nearly the end of the century for more advanced alternatives such as the various kinds of IC engines or steam turbines to be developed, what stopped the engine from finding wider niches than it did?
3) the inventors in fact were hopeful they could offer an engine that was far safer than the steam engine. It was also a lot quieter. But actually the Stirling engine was not completely safe either; achieving high levels of air compression in high performance mode, the air would be heated while a certain amount of some kind of oil was needed to lubricate the works when pushed to high performance forms. High performance Stirling designs could therefore explode, as long as plain air would remain the working gas!
I observed this some time ago in the old ISOT of the Isle of Mann storyline--encountering great enthusiasm for the Stirling engine there, a proponent was claiming that the Stirling offered simple and easy construction, being workable with remarkably low tolerances; high power, and high efficiency at low cost. My response based on my reading was that indeed Stirling engines can offer any of these features, but not in the same model! That is, you can make it cheap and simple, and get useful power at modest levels that way. Or you can refine it so that its potential of higher efficiency than piston steam engines, or even turbine or IC engines, can be realized--but to do that involves very extensive engineering refinement, making far more costly than other engine types. And withal limited, by a narrow band of optimal output; by a narrow range of operating cycle frequency that makes it unable to start from a standstill, limited by rate of heat flow in and out. Such high performance engines are not so cheap, are complex and fussy, and not rabidly responsive to changes in throttle. The kind of Stirling engines that can rival IC or high performance steam engines are comparably or more so expensive to build and operate and are less flexible in key parts of the duty cycle; even where theoretically efficient they are slow to respond to changing demand.
I think the final fatal blow to the acceptance of the Stirling engine in widespread roles was that fuel was cheap, and so saving it was not that large a consideration; what people wanted out of machines like this was more and more power, and they did not mind burning a lot of wood coal or oil to get it.