You need to allow for the long lead times to establish a nuclear...

You need to allow for the long lead times to establish a nuclear plant. They cannot be put in place a year or so like gas plants. The massive construction cost also limits the number of plants that can be constructed over a given period. Hence demand builds up more slowly. The other factor to consider is the time it takes to establish a new uranium mine and put it into production. This is a shorter timeframe but still takes years. Because of the rundown in long term contracts over the past 8 years or so, and low prices causing many uranium miners to go out of business or to close down existing production, then everyone expects a sharp shortfall in the next few years, Even to restart a mothballed plant like Langer Heinrich is expected to take over 12 months, maybe 24. However, the improved price will quickly lead to mothballed facilities being reopened and new mines established and so the price will be moderated even while the increasing number of nuclear power plants grows at a slower rate than mines can be established.
One other factor that increases shortfall in the near to medium term is the rundown in secondary sources of U3O8 such as decommissioning of nuclear weapons and reprocessing of spent fuel along with tailings from processing plants. Political-military considerations may lead to renewed demand for weapons material given the breakdown of limitation agreements while establishing processing plants for tailings is at least as long as building a mine and probably longer (consider the SIlex proposal for Paducah in Kentucky whose output would be equivalent to a large mine).
The cyclicality will not go away because mines can be put into production more quickly than nuclear plants. This will yet again lead global supply to outstrip demand but I agree that we should soon have several years of demand imbalance keeping prices up.
There are plenty of commentaries about the number of nuclear plants under construction and planned but not often with a timeframe expressed for their introduction into service. Delays can be years long and are more common than not; and planned units can be abandoned. Old plants are also being decommissioned without being replaced in the Western nations and even France is reducing its commitment to nuclear.