I do not think that the prototypical scientific method is not valuable in the long term.
In any experiment, there are lots of naturally varying parameters (current phase of the Moon, air pressure, amount of snow on the slope), and there are lots of naturally constant parameters (strength of gravity, room temperature, amount of hydroxyhypotethicol in the solution). There are base and derived parameters. The distances from the sun and the orbital periods vary between the planets, but (distance)^3/(orbital period)^2 is constant.
In the experiment, you measure X and Y. If X vary, but Y is constant, then they probably have no relation. Suppose that we want to find out that is X related to B or C. We control B to vary, and set C to a constant. If X vary, then it is not connected to C, if X is constant, then it is unrelated to B.
In the second scenario, you try to find the minimal set of base parameters that are related to X (growth rate). After some testing, we found that (growth rate) ~~ (initial age). After we found that connection, we can rule out the uncontrolled varying parameters, but there may be a connection between X and an uncontrolled constant parameter. It is possible that (growth rate) ~~ (initial age) times (1 + (amount of hydroxyhypotethicol)), and the first scenario will test these kinds of connections.
It is not enough to find which parameters won’t affect the experiment. It is also important to find out which parameters could affect the experiment.
I do not think that the prototypical scientific method is not valuable in the long term.
In any experiment, there are lots of naturally varying parameters (current phase of the Moon, air pressure, amount of snow on the slope), and there are lots of naturally constant parameters (strength of gravity, room temperature, amount of hydroxyhypotethicol in the solution). There are base and derived parameters. The distances from the sun and the orbital periods vary between the planets, but (distance)^3/(orbital period)^2 is constant.
In the experiment, you measure X and Y. If X vary, but Y is constant, then they probably have no relation. Suppose that we want to find out that is X related to B or C. We control B to vary, and set C to a constant. If X vary, then it is not connected to C, if X is constant, then it is unrelated to B.
In the second scenario, you try to find the minimal set of base parameters that are related to X (growth rate). After some testing, we found that (growth rate) ~~ (initial age). After we found that connection, we can rule out the uncontrolled varying parameters, but there may be a connection between X and an uncontrolled constant parameter. It is possible that (growth rate) ~~ (initial age) times (1 + (amount of hydroxyhypotethicol)), and the first scenario will test these kinds of connections.
It is not enough to find which parameters won’t affect the experiment. It is also important to find out which parameters could affect the experiment.