I think you're using "theoretical" in the way it's used in common speech, to mean "remotely possible". These distributions are theoretical because they are based on theory. The theory specifies conditions, and if these conditions apply, the theory is applicable.
So you don't just figure out what distribution can fit your data. That's a common rookie mistake that's easy in an era where you can easily get a program and ask it to fit 100 different curves to some data. It's possible that you may be able to do this and then inject some domain knowledge into the situation, "Hmmm... this data is biological in nature and it does appear to fit a growth curve that's common in biology, so it gives me some clues as to an underlying mechanism for the data", but without the application of domain knowledge to the problem, you're just doing curve-fitting voodoo.
Rather, a scientist looks at the conditions under which the measurements were made, at the underlying mechanisms that are plausible, and chooses distributions which would be applicable. Of course, a distribution is used because there is variation and uncertainty in the data, so you shouldn't expect that every single point of the data should fall exactly on some curve
Since things don't match exactly, are the calculations all wrong? Yes. The question is "how wrong and for what reason?" If the answer is "not very wrong, and mainly because of small measurement errors", it's good enough. No application of any theory is going to fit perfectly in the real world, but if properly applied it will be close enough to do what you need to do.
Which raises the question, "what do you intend to do with the data?" If you're happy assuming that you've measured the entire population with no error, and you will not speak of anything outside of the population, and don't care to speculate on underlying mechanisms, you don't need distributions. If you want to measure the heights of the members of your family (the population) and make statements like "the tallest person in our family is X tall, and the shortest person is Y tall, and half of the people in our family are taller than Z and half are shorter.", great for you. No need for distributions at all -- assuming you're ignoring measurement error, of course.
If you're going to go beyond this, if you can't measure the entire population, you'll need to use distributions to account for variability and uncertainty. Not arbitrary distributions, but ones that are applicable based on a knowledge of your goals, your data, your assumed mechanisms (model), etc.