You seem to have it backwards with regards to what science (in particular physics) is doing. Where mathematics, logic and to some extend religion build a universe from the ground up, so where they start from a ground truth (or a whole set of them) which are then just assumed/believed (axioms) and then mixed and matched into something complex. Science is more or less taking the opposite route.
In science you look at a world that is incomprehensibly complex and first of all make observations and measurements and then try to find patterns in them and then describe those patterns. So the reason why force is equal to mass times acceleration is because that's what we observe. You observe that for example an otherwise resting object is being attracted/repelled (by e.g. gravity) and that this attraction (force) is proportional to the mass of the object and that if you look at the ratio of force and mass you end up with a constant.
So physical formulas are essentially the mathematical form of story telling. You have a bunch of facts and key events and you weave them into a coherent narrative. The beauty is that the result is short, easily memorable and comprehensible (unlike the chaos that are your real life data points). The downside is that it is wrong.
So you could call these stories an answer to the "why" question, but as you've realized yourself they technically aren't, because they don't actually describe "why" something is happening and quite frankly don't even bother to do so, they just describe a model that would produce similar results.
Also what does it mean that they are WRONG??? Well the proportionality of mass and force and the equal ratio isn't exactly like what you expect in mathematics where F_1/m_1 = F_2/m_2 = F_3/m_3 = ... F_N/m_N and so on, but in reality it's closer to idk having a set of measurments like [10.2, 9.7, 9.1 , 9.0, ...] where you end up with ~9.5 kg*m/s². So rather than dealing with inevitable certainties of calculations you more or less eyeball a curve that fits your data points. I mean nowadays you no longer literally eyeball it you could just take a simple template of a formula, idk a polynomial (a+bx+cx²+dx³+ ...) let the computer guess the parameters and measure the difference between the curve and the real world data, rinse and repeat until the error is small enough for your liking. So as a result, unless axiomatically defined, scientific constants are NEVER just a value, they ALWAYS include a margin of error (usually something like the average discrepancy between the idealized curve and the real world data).
Now after several iterations through different narratives, improvements in measurements and so on, we end up with something that is quite useful in our everyday life.
And another feature of these models is that they don't just summarize the collected data points, but due to being continuous and not limited with respect to their parameters you could also predict what the results should be for values that are NOT in our data set.
Which enables us to look into the future (timetables, weather predictions, etc) or to estimate how things will behave that we haven't tested yet.
where it's often times these situations of the theory breaking (large (enough) discrepancies between prediction and reality) which reveal something interesting about the world and enables us to improve our estimates.
Again with many asterisks, like it's a pretty decent approximation to say the earth is flat (if you're not traveling far). While if you traveled in all directions and find out that you're back to where you started from you might realize that there's something wrong with this idea. So they might beat random guesses what comes next, but the further you deviate from the data that the model is based on the more likely you'll find something "interesting".
Now as a result of all these things you might accidentally still embark on a quest to find the "why". Because in your attempt to build models of phenomena and maybe even meta models of the models you've build, you might produce chains of cause and effect which might already suffice the quest for knowledge of some. But they ultimately are deterministic, they give no answer for a reason or purpose, things happen because they happen and if our model could describe all the things happening that would be sufficient.
Also worth noting, that doesn't need to be a feature of reality, it's more of a feature of our models of reality, because with regards to compressing data points and making predictions, it's quite counter productive if you'd end up with something unpredictable and indeterministic. Like sure a religion might be fine with having things be the result of the agency of a god, but if you want to describe how things are happening, this would mark a brick wall that you'd crash into.
So in that regard indeterminism just isn't that nice for this method of epistemology. Like not being able to predict the outcome makes it kinda tricky to derive a formula for the outcome. Like sure on the macro scale, you can deal with that because while the outcome of an individual experiment is unpredictable, the outcome of millions of them is predictable.
Also with regards to the world formula. That's a tricky thing. Like on the one hand if you had this one effect that is underlying all the other effects and makes all the rest just a consequence of that one thing, would certainly be a major accomplishment in the quest of creating an understandable universe. The problem is, have you actually reduced the complexity of the universe or is that formula still as complex as the universe used to be? Also how good does it perform? Like it's technically not hard to create a world formula e.g. 42. Though while it might be working in some domains, quiz questions concerning the Hitchhiker's Guide to the Galaxy, it might be considerably less useful in most other domains... So it's not enough to make up a theory of everything, it also needs to be simple enough, have a low margin of error and ideally have a somewhat uniform margin of error. Like it is pretty awful when the theory of everything works for close to everyone but you and you're just discarded as "within the margin of error".
I mean that's where the debate about pseudoscience usually starts with, that you end up discarding real world evidence in favor of the theory rather than the other way around.
So TL;DR that instinct stems from the fact that physicists are not really in the business of "why" but in the business of "how".