While a NDRB would solve some problems, I really don't think it would do as much as "advertised." I have included some discussion below.
First off, a Google search says the NTSB has approximately 400 employees. While that may not be 100% accurate, it can provide a starting point for the discussion.
We would have to think that a new agency just starting out would not have that many employees. Or, would NWS be required to give up some of its employees or funds to start the NDRB? It's a question worth asking, as we see examples of horse-trading all the time in Congress. ("I'll only give you this if you are willing to give up that.")
With a (relatively) small number of employees, a NDRB would not be able to check or verify every tornado warning, much less all the severe thunderstorm, flash flood, and winter storm warnings. What is to be done when a storm (or maybe it was a tornado) causes damage and the public, emergency managers, and news media want to know which it was? Will they be satisfied to wait a few days or more for an answer until an NDRB person can make it to the scene? And how much evidence will be gone/cleaned up before the person can get there? Demolition of many badly damaged houses in Vilonia, Arkansas, was well under way two days after the tornado occurred. I can recall cases where most of the damage was gone within ONE DAY after a storm or tornado occurred in a fairly small, rural area. And, remember, the NTSB does not allow any of the "parties" to one of their investigations to release information to the news media. If NDRB is modeled after NTSB, after a big storm occurs NWS will not be able to give media interviews or go over radar data with the news media. So sorry, but the media will just have to wait a few days until someone from NDRB can make it to the scene.
Under special Department of Commerce rules, any NWS employee can give an interview to the news media (though this could be limited by local rules) as long as they stick to the current or past weather or the forecast (i.e., no discussion of things like the President's budget or similar topics). NTSB doesn't allow any such thing.
Also keep in mind that NTSB must "investigate" every aircraft accident, whether they even go to the scene or not. For some of the "smaller" events, only an FAA person goes to the scene (as they note in some of the their NTSB Newsroom posts). And NTSB certainly does not go to or "investigate" every fatal car accident. If NDRB does not go to a damage scene which might have been a severe thunderstorm but might have been a tornado, how are statistics going to be compiled on Lead Time, False Alarm Ratio, and Probability of Detection? (Yes, I know the system is not anywhere near perfect as it is. Some NWS offices will take the word of an emergency manager, whether that person has any training in surveying damage or not.)
Next question: Who is going to compile and publish Storm Data? If NDRB doesn't go to questionable scenes, who makes the call? Right now, entries for Storm Data are supposed to be submitted two months after the end of a given month (Example: Each office is supposed to send in Storm Data for January by the end of March. (That deadline is not always met, and there have to be some exceptions like for Hurricane Katrina.)
But let's remember that NTSB says their investigations may take 12 to 18 months and they don't always finish in that time. Do we want to model NDRB after this part of NTSB?
And let's discuss a topic that Mike Smith has expounded on. What is to be done when there is controversy over whether a tornado warning should have been issued and/or the time it was issued? As noted above, there is no guarantee that a NDRB person would even go to the scene if it's a "minor" event (what *might* have been an EF0 or EF1 tornado with no fatalities). And how long does NDRB get to study the matter? Hopefully not the 12 to 18 months cited in the previous paragraph, as the time for any hoped-for corrective action would have long-since dwindled by then.
Darn. Maybe I should have put "tl;dr" at the beginning of this essay. Suffice it to say, I've given this a lot of thought since Mike brought up this idea and I'm sure I've left out some things that I have considered in the past. In the NWS, I did storm surveys for more than 20 years. Also, I worked on the Directive that spelled out how to compile and write Storm Data entries (a person in NWS HQ was, of course, the leader of these efforts and I was one of two field office meteorologists who was picked to work on writing these "rules" that NWS offices had to follow). The last of these Directives that I worked on before retirement was more than 100 pages long, so every update was a massive undertaking that required plenty of work at home. I also compiled the local severe weather statistics for the office that I worked in. (The Meteorologist in Charge was not necessarily always happy with the storm surveys that I did or the severe weather scores that I compiled, but I was going to do things honestly, no matter what. And I never got overruled, either.)
I just hope that the issues (and potential pitfalls) that I cited will be taken into account if a NDRB comes to pass.
I'll say only one more thing here -- about radar outages. Since the WSR-88Ds were installed, they have been updated a number of times. This is fortunate since they are already at the end of their originally-expected lifespans. Like any piece of electronics gear, failure can occur unexpectedly, no matter how much routine maintenance is done. The bull gear failed on the radar at the office where I worked. It was the first in the nation to fail. For those that are not aware, the big, expensive parts, like the klystron, are not kept at local offices. When there is a failure, the part has to be flown in from Norman or Kansas City. This obviously leads to outages that lasted longer than we wanted. The flights often arrived in the evening and a courier service delivered the part to the office, no matter what time of night it was. And the shift leader then called an Electronics Technician(s) to come to the office at night to install the part. In our case, there was an Air Force Base that was also using the radar, so there was even more urgency to get it fixed.