Just a bunch of guys talking about watches, im not arguing an hope Im not coming across that way.
Because tolerances grow and shrink differently for different metals while being subjected to vibration and positioning changes.
I'm not trying to argue either, but at the same time I have spent a lot of time studying this stuff and putting into practice, so in a sense I'm challenging your statement.
Here's my "long answer" as to why, and I know some of this stuff is basic information, but bear with me.
A typical watch movement has 5 gears in constant mesh, or "wheels" in watch parlance. Although not often called a "wheel" the first of these is the mainspring barrel, which of course carries the torque of the unwinding mainspring.
This meshes with a wheel traditionally called the center wheel. Historically, the center wheel was quite literally in the geometric center of the movement, and directly drove the minute hand. Consequently, it makes one complete rotation once per hour.
Moving on down the train, you have the 3rd wheel, which has no fixed rotational speed, and then the 4th wheel, or sometimes called the "seconds wheel". Again, this traditionally drove the second hand directly, and consequently rotated once per minute. There again, from the center wheel to 4th wheel, there is a 1:60 increase in rotational speed.
Meshing with the 4th wheel is the escape wheel. This wheel, in combination with the pallet fork(in a lever escapement watch, which is most everything now outside the Omega Coaxial), both stops and starts the train, and also transmits power from the train to the balance wheel. Typically the escape wheel has 15 teeth, and advances forward by one tooth for every oscillation of the balance. You can do the math on its rotational speed-on the 18,000 bph watches I normally work it rotates once every 3 seconds.
I go through all of this for a reason. The correct sideshake(spacing) of all of these wheels is critical on set-up, and ideally they "roll" over each other without the teeth bottoming out. None the less, though, expansion or contraction of these with temperature isn't particularly significant because rotational speeds are so low and torque is(relatively speaking) quite high.
If the escape wheel does change appreciably in size, it can affect the pallet stone engagement which does affect balance amplitude, but I quite literally have never seen that become an issue on watches of any size.
You then, by means of the pallet fork, get to the balance wheel. This is the harmonic oscillator in combination with the hairspring that is the ultimate timekeeper in the watch. The "beat rate" of a watch describes the oscillation frequency of the balance wheel-i.e. 8 times per second in a 28,800bph watch. The balance wheel, for most of its rotation(generally 220-240º in each direction-this is a design parameter of the watch and is called the amplitude) is completely free spinning. It ONLY interacts with the balance wheel through a few degrees of rotation(called the lift angle, BTW) by way of the roller jewel or impulse jewel. During this period of interaction, it "kicks" the pallet fork over, which allows the escape wheel to advance by one tooth, and as the escape wheel advance it feeds energy back into the balance wheel. This allows it to reach a steady frequency.
I've gone through all of that because, again, the oscillation frequency is key to timekeeping, and in particular having a consistent, repeatable oscillation frequency. It is the fastest spinning wheel in the watch, and as it is mostly freely spinning on just its pivots, a lot of things can affect its velocity, or more importantly the amplitude. One of the first goals is to have the balance wheel be isochronic, or have the frequency remain constant regardless of amplitude. I'm ignoring the temperature elephant in the room now, but things like varying friction across positions, a balance wheel out of poise(not balanced around its perimeter) or a lot of other things can affect amplitude, and isochronism is largely kept in check by properly formed hairsprings. Some hairspring designs are better at this than others. The helical hairspring is the gold standard for this, but it's far too thick for wristwatches, or even most pocket watches(I do know of helical spring pocket watches). It's mostly seen in things like deck watches and true chronometers. Next down the list is the overcoil hairspring, which is still used some(by Rolex in particular). Flat hairsprings are worst, but careful forming and newer tricks like the "dogleg" terminal curve are better than a plain, simple flat spring. Conventional regulators are a huge issue as well, as the interaction between the hairspring and regulator pins can be problematic. Consequently, freesprung designs, or designs without a regulator, are preferred but are more difficult to adjust the timing. Rolex almost universally uses freepsrung designs, and regulation is accomplished by tiny nuts on the balance wheel(called "Microstella nuts") that change the moment of inertia and are adjusted with a special wrench.
In any case, temperature does affect the balance wheel. The oldest watches used a carbon spring steel hairspring and a monmetallic flat balance wheel typically made of steel or gold. There are two big issues with this-thermal expansion of the balance whee and change in the spring constant of the hairpsring. At high temperatures, the wheel expands and the spring becomes less elastic, both of which slow the rate. At low temperatures, the opposite happens-the spring becomes more elastic and the wheel smaller, so the watch speeds up.
The first attempt to fix this was the split bimetallic balance wheel, which is laminated steel and brass(usually). At high temperatures, the ends of the arms curl inward decreasing the effective diameter, and at low temperatures they curl outward to increase the diameter. The idea is to counteract the change in spring elasticity. This was a complicated process that often involved moving weight around the rims(using brass or gold screws) to find the right spot, and it still left residual "middle temperature error." Adjusting a split bimetallic watch to temperature is not one of my favorite things to do.
Back in the 1930s, the Swiss developed a material called Elinvar, or short for "Elastically Invariable." As the name would suggest, the spring constant stays more-or-less the same regardless of temperature. This was used in combination in some cases with Invar, which is an alloy with a low coefficient of thermal expansion. Middle temperature error still hangs around but it can amount to a couple of seconds a week. The late George Daniels tried a few different techniques, including a few designs of bimetallic balance. He finally settled on using a set of four bimetallic "fingers" facing inward that would iron that error down to a second or so a week. That's really splitting hairs, though.
In any case, the long and the short of it is that modern mechanical watches really aren't affected by temperature, or at least normal temperatures to which they're likely subjected. IIRC, COSC does include temperature testing also. The rate of change in temperature is not going to be different enough to matter cased or uncased. In fact, the case can add enough thermal inertia that temperature swings will be less extreme and conceivably a movement COULD(not necessarily will) rate better cased than uncased. I'm having a hard time thinking of a situation where an uncased movement would rate worse than the same movement cased.