There is a common misconception, that we could solve a lot of the problems with reactor construction, both large and small (though in particular the small ones) by building them in subsurface pits. I’m assuming the person who thought up this one has never dug a hole in his back garden! If you have, you’d know that digging a hole is not as easy as it seems. Firstly, the soil type has a big bearing on things. Depending on where you live you could be looking at thick sticky soil that difficult to shift, loose gravely soil that collapses easily or rocky earth, that rapidly turns into bedrock (so after a while you’re not digging any more but blasting!). As we need to put foundations down under out reactor to suit the soil type, and probably piling too (due to its weight), this means we essentially need to design each reactor’s containment vessel individually to suit local soil conditions, which increases costs.
Another problem is water intrusion, as anyone who’s ever dug a pit, then gone in for lunch, come back out and found it full of water will know all about! Our reactor “pit” needs to be designed like the hull of a boat to stop water leaking in and flooding it. Doing that with concrete, particularly thick section of it, is always difficult. The fact that the reactor will be generating heat complicates things as it raises the risk of subsidence or settlement cracking. While this can happen if the reactor is on the surface too, putting it under ground level “complicates things”.
In general with any construction project significant efforts are made to reduce the amount of earth movement required to start construction, not increase it, as lots of earth moving nearly always results in delays, hold-ups and ultimately higher costs (not the least of those being the cost of hiring out of earth moving equipment, those guys charge an arm and a leg!).
Overall, except in a small number of narrow cases building reactors this way will often work out as more expensive and slower than just putting the containment dome above ground.