I think the changes you cited (less damage due to high precision use of low yield weapons) make it on balance more likely they'll be used.
The real barrier to nuke use is gaining entry to the club. U235 enrichment, Pu239 synthesis, implosion, initiators, etc. In contrast, the entry barrier to precision delivery is small and diminishing.
If you're new in town (IN, PK, NK), your noob inefficient, unoptimized weapons can be really effective if precisely delivered. And it doesn't necessarily mean ballistic delivery. Moves the "unthinkable" threshold downward. It's worrisome.
Then, likely, presto, bingo, the intel agencies of the more advanced countries will notice what is going on inside the building just from what is on the purchase orders going outside the building. Then have some drones and/or satellites fly over the building with some neutron or gamma ray detectors or some such. Then have a little chat with the leaders of that little country.
I'm not sure it would be easy to hide such activities now.
And if they do get some fissionable materials, then they would have to test a bomb, and can't hide that.
A smaller opening volley doesn't feel like any increased incentive to initiate said volley.
You do it and you'll get to watch the US, China and Russia briefly join forces and annihilate your infrastructure with extreme prejudice - with options to use their arsenals if anyone suspects you'll try to while this is happening.
And sorry, I see I wasn't clear about the precision delivery aspect.
While newer members of the nuclear club may not have the greatest in precision delivery, that capability is almost completely a matter of electronic technology. Which means it's getting easier and cheaper in the same way that our cheap smartphones eclipse yesterday's mega$ supercomputers. I'm sure IN is already there, probably PK as well. NK, not so much. Yet.
That in turn makes unoptimized weapons with only say, 5kT yield very useful. Such "tiny" yields diminish the horror factor associated with using nukes. 5kT is way more "imaginable" - it's only 250 truckloads of TNT (single big rig load of 40,000 lbs).
In short, precision delivery makes low yield (cheap) bombs useful. That diminishes the restraint underpinning MAD.
https://www.youtube.com/watch?v=OTE_Eshm2xw
(I say supposedly as the only articles about this as on conspiracy-theory sites, but it looks pretty realistic)
Another sign that this is BS is the fact that "bunker buster" and "neutron bomb" make no sense together. A neutron bomb is designed to decrease the explosive force while increasing the amount of radiation produced, with the idea that tank crews are easier to kill through radiation (which tank hulls don't protect against very well) than through blast (which tank hulls are great at protecting against). But radiation is a bad weapon against underground targets, where each foot of soil acts as shielding to reduce the amount of radiation by a factor of something like three. To destroy bunkers, you want blast, not radiation.