To what extent does the quality of data play in the accuracy of a model? I’ve worked with businesses where I am provided with a data set that I know is inadequate in terms of its signal with respect to the measure in which I am trying to predict. No matter the extent to which I perform data engineering to create new variables, or the extent to which I experiment with new models or new model parameters, the performance metrics of the models I use will always approach a ceiling point due to the limit of the nature of the variables that is being used. Hence the question I pose: whether one should attempt to perform feature selection, model selection, hyper parameter optimisation IF there exist this constraint?

An extreme example might be determining the name of a dog’s owner based on a photo of the dog’s tongue. You’re missing critical information from the veterinary records that associate the dog with a human. With such information, you might be able to get the right answer every time.
It can be the case that you simply lack the information to make accurate predictions.
Consider an outcome that is totally determined by the two feature variables (so this outcome is entirely predictable, in some sense), which are independent on each other. If you only have measurements for one of those variables, you’ll never reliably make accurate predictions. Since the two features are independent, you cannot even wrangle information about one out of the other. This would be the low signal-to-noise ratio that you mention.
If your features are related, perhaps you can wrestle with observed features to glean insight about what the unobserved feature would have been had it been measured, perhaps at the risk of overfitting.
However, if you feed a model garbage data (tongue picture), it should be expected to output garbage predictions (inability to predict owner’s name).
