This ended up pretty long, and is of course only my own opinion, but on the remote chance of someone wanting to read it anyway, here goes...
There is a strong hint in the term "normal category [aircraft]". It has been determined, from long experience and for good reasons, that a certain set of rules and standards is required to achieve a sufficient level of safety and order during such flying as falls under the restrictions of what you are allowed to do with such an aircraft. The safety of the pilot, the passengers and third parties need to be considered, and regularity and other such matters need to be taken into account for the flight not to impede the safety and regularity of other activities.
An aircraft is a normal category aircraft (if it is not some other certification category, such as utility or transport), unless some exceptional circumstances dictate that it should be exempt from the normal category regulations.
There are excellent reasons why the rules relating to normal category aircraft need not apply to certain types. The rules might not be practical or reasonable due to the very special nature of the aircraft, as in the case of experimental designs and home-built aircraft. Vintage aircraft would be impractical to redesign, maintain and fly according to normal category rules; even grandfather clauses must eventually expire. Aircraft might simply be too small for the rules to be practical, as in the case of ultralights.
But if an aircraft is designed to perform, behave, and have the same capabilities as a normal category aircraft, and indeed is being marketed as a replacement for or alternative to normal category aircraft, then how does one argue that it is so exceptional that it should not be treated like a normal category aircraft? One would have to argue that it does not actually have the same capabilities as a normal category aircraft, that the normal category rules are unreasonable due to this reduction in the stated and desired capabilities, and that it therefore should be exempt from the normal requirements.
When an aircraft is permitted to fly without being certified in the normal category (or some other certification category), it is accepted that the degree of safety required in normal flying can not be guaranteed. The key word here is guaranteed; the non-certified aircraft can very well be as safe as or safer than most normal category aircraft. But the certification regulations ensure that sufficient safety is not merely achieved, but that it can be reliably demonstrated before the accident statistics arrive. The regulations also ensure a uniform level of safety; if the regulations are followed, there should be no outliers, such as poorly designed or maintained aircraft, that have a much lower safety level than other normal category aircraft.
Therefore, statistics showing that non-certified aircraft has an equal engine failure rate as normal category aircraft does not demonstrate an equivalent level of safety. If normal category aircraft in general display a certain statistical failure rate, one can reasonably assume that a particular normal category aircraft should be at least as safe, since they are all certified to (roughly) the same rules. The same can not be said for non-certified aircraft, due to the widely differing design standards of such aircraft.
To offset the increased risks from not following the normal category regulations, mitigation strategies are needed. Using the PAVE model, for example, the Aircraft element can be considered to always be marginal, requiring the Pilot-in-Command, EnVironment and External pressures elements to be optimal to keep the overall risk in check (i.e., night or IFR flight becomes rather questionable). Limitations on the carrying of passengers (especially for hire) or where and how the aircraft can be operated ensure that no third parties are exposed to the increased risks or are otherwise negatively influenced.
Or, a subset of the standard category rules can be required to be met by the non-certified aircraft, to the extent that it is being operated similarly to a normal aircraft. Carrying transponders in controlled airspace falls in that category, as would requiring IFR certified avionics for IFR flight.
Keeping the above in mind, my conclusions would be:
1. While sufficient safety can be achieved flying a non-certified aircraft at night or in IMC, that safety can not be guaranteed. This uncertainty adds to the uncertainty in, e.g., the pilot's safety level, which can of course never be guaranteed. It would also be quite hard for the pilot to have a good estimate of the aircraft's suitability for night and IFR, without the benefit of certification. Let alone the unsuspecting passengers...
2. If non-certified aircraft shall be flown at night or IFR, it would need to have certified avionics. This begs the question,
2b. Is that practical? For instance, how does one go about certifying an avionics installation in an uncertified aircraft? Under what regulations would it be done, and would the costs be manageable?
3. What is the motivation for the aircraft not being certified? In some cases it is already questionable why it is a non-certified aircraft rather than a normal category VFR day only aircraft, but the disparity between the intention behind the exemptions from normal category regulations and the actual use of some of these aircraft becomes even more obvious when they are flown at night and IFR.
The ability to fly non-certified aircraft is a great thing. It permits aircraft to fly that otherwise could not be flown, under suitable conditions, and it helps aviation progress by enabling experimental designs to be built and tested. The advances made through those experiments can then be included in normal category aircraft, as illustrated by, e.g., Cirrus and Diamond aircraft.
But when the lack of certification is only a cost saving measure, where an aircraft is to all intents and purposes a normal category aircraft that has been left uncertified to keep the costs down, then it can hardly be called progress. The normal category rules are there for good reasons; not following them in exceptional cases is fine, but disregarding them for normal aircraft is not.
So when some see “permit aircraft” as the way forward and the future of general aviation, I almost entirely disagree. I do agree, to the extent their existence aids the progress of normal category aircraft. It is also true that very many pilots can not afford or do not want to pay the cost of flying normal category aircraft, thus preferring other forms of aviation. But non-certified aircraft are not a replacement for normal category aircraft, and that was never the intention behind the exemption from normal category rules.