There should be a LOT of nuclear accidents
In fact, the thing behind all that weapon regulation is the desire to limit high energy production equipment in hands of, umm, civilians, because it's energy influx that kills, as a principle, also such energy producing things could be employed to do various criminal actions, like breaking into or out of somewhere, like a bank for example. So, with average user being able to land their hands on a nuclear reactor, or at least a set of fuel replacement, there will certainly be groups that would either threaten or employ nukes as a means of doing their own business, starting from assassinations and ending with revolutions.
So, you might compare wielding a bit of uranium to wielding a weapon, but a really unreliable weapon that can not just shoot down a certain target, but also eliminate its vicinity together with the wielder (at times). That said, assembling a nuke in one's garage is not an easy task, you need quite a lot of ordinary explosive to even have a chance to not get a "nuclear fizzle" or a meltdown of your valuable uranium storage into a pool of radioactive magma, and you need to actually align that explosive so that the uranium gets correctly imploded to shift phase (assuming they know what is a phase of uranium) and go supercritical. But with the abundance of uranium across the society its accessibility will be high enough for some people to try and get obliterated in the process, resulting in a nuclear accident.
The reactors are also not completely accident-proof
Let's say your house reactors are controlled by a PIC of sorts that's powerful enough and programmed so that it can shut the reactor down in case of something really weird happening in the active zone. It's been tested for safety and has a secondary or tertiary system to prevent the meltdown. It does NOT accept external interference, and might only have some maintenance access for whoever changes its fuel, which should happen pretty often (and I really wonder what do they do with the nuclear waste - it'll grow to extreme amounts over that many reactors!). But now let's assume that some ISIS-like organization has learned about a weakness in its algorithms or some human-originated weakness in maintenance of a certain one, and was able to reach it and initiate the meltdown. With our current stance, reactors are protected by military, but in your world there will never be enough military to protect the entire set of reactors, so there will be some vulnerable objects that could be melted down. Aaaaand you've got a whole Chernobyl or Fukushima-level disaster in a certain house, that destroyed that one and damaged several other houses nearby - potentially initialing a meta-chain reaction in form of one or more of affected reactors to also go meltdown, which is quite likely because if a reactor would be in a center of a radioactive zone where a human can't stand without dying, it'll become out of maintenance and any single malfunction would be enough for it to go down too (at least it'll just shut down, but who knows what would happen next).
There's more - a nuclear accident is a something that regularly happens at various nuclear power plants, even while operated normally, even venting off some of the second ring steam due to a pipe/valve breach that happens over time counts as one, as that steam would be slightly radioactive due to being closer to actually radioactive media that was in contact with the active zone. You might check INES scale with examples of what can happen on a nuclear power plant that's counted as a severe accident, together with their average frequency per reactor, then multiply over your numbers that heat up literally every single building. This alone would number at least several dozen per day with expected number of reactors in your society.
Intel/cops will not be able to stop everyone
As in real life, even with some of the modern systems of crowd control (hey China!), there will always be people who are able to plot crime and succeed in its execution, no matter if they get caught afterwards, a crime related to a nuclear accident, if succeeds, leaves an accident up to actual Chernobyl, depending on what had really happened. Safety concern should quickly rise over several first accidents involving house reactors, to the point of abandoning the entire idea, after all, no one wants to go to sleep in total safety only to find out that they've got irradiated to fifth degree cancer over the night because someone did a boo boo. And the citizens won't really care that those who obliterated that neighboring building were terrorists, burglars or incompetent plumbers; the rage will eventually focus on those who planted those nukes first and foremost.
On top of that: nuclear-powered cars ended up ridiculously superfluous
A nuclear reactor of modern design is a VERY slowly alterable power generator, that is, you can't stop and start it at will, you can throttle it but it'll take hours, and while it's in your garage it still consumes fuel at about the same rate as while driving 300mph. Cars are designed to run part of the time and stand still the rest, while also having relatively low power demand (100 horsepower is just 75 kW, rarely a truck has 1000HP, let alone personal cars), and the reactors were producing about an order of magnitude more. This is actually one of the reasons (aside safety) that made reactors be viable only on large installations like icebreaker ships, military subs, airplane carriers and the like, even in military - like, no nuclear engine on tanks or airplanes. Building a reactor for a large house (say a skyscraper) looks feasible by power demand, but with it being slow to change its output it became easier to build a power grid to transfer electricity to places with high demand, reducing wear load on nuclear plants, reducing start-stop load on coal or gas plants, etc.
Nuclear waste adds to number of accidents by means of polluting environment
Even if everything went well for long enough for the govt to actually start building autonomous houses, there is a problem unsolved here, in nuclear waste disposal. The isotopes produced by uranium fission have a half-life of over 60 years (Cobalt-60, Cesium-137), are aggressive enough to damage facilities designed to separate the spent nuclear fuel, also any structures that contained the fuel (steel, zirconium, whatever else they use) become irradiated over time and infused with radioactive isotopes with highly various half-life, and all this should be somehow put away from the living, or else they would soon turn dead. With each modern water-based reactor requiring refuelling about once per 2 years, and your world's reactors being about the same internally, your society would generate so much nuclear waste that will not be able to be contained anywhere, and even recycling facilities that could retrieve leftover uranium out of spent fuel will be overloaded, as the process is literally nano-tech thus very energy consuming and very slow as well. Note that spent fuel still generates heat and radiation over years required to reduce their initial radioactivity to levels that allow its transfer, demanding special areas near each NPP to store their own spent fuel, and if something happened there, it also counts as an accident and usually requires HazMat interference to clean up.
In total, nuclear fuel in this amount is too unsafe to calculate
Even without destructive human interference, your world is about to blow up with this input data, either from the amount of "normal wear and tear" that the reactor system undergoes, or from the accumulating amount of radiation coming from spent nuclear fuel.