Exchemist has mentioned the most important point, dropping pasta into defined temperature creates the most reproducibility. Now there is quite some chemistry related to pasta cooking and generally speaking, the first process is controlled by water penetration, starch gelatinization and protein coagulation.
These steps are all temperature dependent but not all aspects are impacted equally (https://doi.org/10.1016/j.jfoodeng.2007.03.018). For example water penetration occurs at low temperatures, but protein coagulation generally requires higher temperature for homogenous coagulation. Yet, that is also dependent on the way the gluten network is developed during the production of pasta (https://doi.org/10.1080/10408390802437154).
Another aspect is the rate of starch gelatinzation to protein coagulation. If coagulation dominates and is done faster than than gelatinzation, starch particles will be trapped in the gluten network resulting in more firm pasta (which is usually desirable). Conversely high starch swelling with an incomplete network allows starch to escape to the surface (and cooking water) which results in soft and sticky pasta (https://digitalcommons.usu.edu/foodmicrostructure/vol2/iss1/2).
As gelatinization starts at lower temperatures, cooking from cold will release more starch. That all being said, for dried pasta it generally does not matter unless it has a large surface (e.g. fettucine) where the released starch can make things rather sticky and where cooking in boiling water accelerates protein coagulation. Otherwise, one can do the opposite for example soak pasta at low temps (before starch gelatinization, so <45 ish or so C). This takes care of the water penetration part while gelatinization and coagulation does not occur yet. You can then then just heat it up (e.g cook in sauce) to rapidly induce coagulation without the release of excessive amount of starch.