In fact, there are a lot of standard designs. There's just not A standard design.
The issue is we build 1 or 2 plants at a time with a given design and by the time those plants are finished (10+ years) new regulations and new standards are in practice (see Gen II vs Gen III vs Gen III+ vs Gen IV reactors).
The good news is that Gen IV reactors, if approved, are much cheaper to build than Gen III/III+. The bad news is nobody wants to build them.
Generation III reactors were also promoted as more affordable than Gen II before they had actually been built. Anyone can build a great reactor on paper. I would evaluate Gen IV cost and schedule numbers after they start generating power.
In 2014 Westinghouse still touted high confidence in affordable, predictable construction for its Generation III AP1000 design:
From the outset, the AP1000 PWR was designed to reduce capital costs and to be economically competitive with contemporary fossil-fueled plants. This requires lower overnight construction costs and higher confidence in the construction schedule.
The AP1000 plant reduces the amount of safety-grade equipment required by using passive safety systems. Consequently, less Seismic Category I building volume is required to house the safety equipment (approximately 45 percent less than a typical reactor). The AP1000 plant’s modular construction design further reduces the construction schedule and the construction risks, with work shifted to factories with their better quality and cost control as well as labor costs that are less than those at the construction site.
This also allows more work to be done in parallel. The use of heavy lift cranes enables an “open top” construction approach, which is effective in reducing construction time.
With new computer-modeling capabilities, Westinghouse is able to optimize and choreograph the construction plan of an AP1000 unit in advance by simulation. The result is a very high confidence in the construction schedule.
In actuality, AP1000 construction went so far over budget and behind schedule that it bankrupted Westinghouse 3 years later:
No. How could you even think there is any logic in such a question?
Nuclear plants are vastly different from PV plants. PV involves a large number of loosely coupled modules with very large amounts of redundancy. Malfunctions in individual components do not affect the system as a whole. Contrast this to a nuclear plant, where redundancy when it exists is on a much smaller scale. The parts in a nuclear plant must be constructed with much higher reliability in order for the plant to operate. The consequences of failure are much higher.
The difference is a solar farm consists of 4 million identical modules and a quarter billion identical cells. If a cell is faulty, it decreases output of that module by 2%. If a module is faulty it either decreases the string output by 5% or costs $80 and 15 minutes to replace. If many modules are found to have a long term fault later, repowering comes at a cost penalty of about 1c/kWh. Building terawatts of solar involves trillions of identical cells, and trillions of trials to practise making them cheaply with zero penalty for iteration.
A nuclear reactor consists of many thousands of bespoke parts. If one is faulty, at the very least the whole thing is shut down while millions are spent replacing it, or possibly it kills a lot of people. Building terawatts of nuclear involves making each part thousands of times, and the penalty for iteration is thousands of man hours for validation as well as potentially shutting down every power plant with that part. If there is a major systematic flaw you are out 5-20c/kWh and years of output.
The issue is we build 1 or 2 plants at a time with a given design and by the time those plants are finished (10+ years) new regulations and new standards are in practice (see Gen II vs Gen III vs Gen III+ vs Gen IV reactors).
The good news is that Gen IV reactors, if approved, are much cheaper to build than Gen III/III+. The bad news is nobody wants to build them.