C has a division operator, despite the fact that plenty of CPUs (ARM, for a common example) don't have a divide instruction. Typically, the compiler generates a call to a runtime support library (e.g. libgcc) with division functions for various datatypes, and yes, those functions typically involve some looping.
That's true, and it's also a bit of a nitpick. How many of us actually work on multiple architectures or with different C compilers? For most systems-level stuff, you are simply using gcc on x86 linux, with plain-vanilla glibc, so honestly, I know what that div op is going to map to. If you've been at this for a while, you know what to expect when you write a simple for loop vs some pointer arithmetic. And if you happen to be an ARM guy, you probably are familiar with all the quirks of your platform as well.
I agree that experience will develop an intuition for how C statement map to assembly. But experience is no replacement for standards -- no implementation defines the language. In most cases, it's more useful to reason about the guarantees within the language rather than inferring what the compiled assembly will be. Possible? Yes, if as you said development is on homogeneous platforms. Painful? If you need to know how 5 compilers act instead of 1, I suspect so.
The point is not to know the actual assembly. The point is that you'll never run an operation that might take a non-deterministic amount of time to run.
Contrast to, say, Python (as an obviously exaggerated counterexample). Just calling a function in Python means performing a lookup in a hash table.
Dividing one 32-bit number by another is a constant-time operation even if on some machines (e.g. ARM) it is implemented as a loop. This is what matters. Raising a number to the nth power is an O(log n) operation.
To decode? Why does the user care how long it takes to decode, they care how long it takes to run. We can provide upper bounds for exp, sin, and erfc too.
C has a division operator, despite the fact that plenty of CPUs (ARM, for a common example) don't have a divide instruction. Typically, the compiler generates a call to a runtime support library (e.g. libgcc) with division functions for various datatypes, and yes, those functions typically involve some looping.