Business reason: When you're in the business of building software, people are your biggest expense. You want to waste their time as little as possible.
Dev reason: tight feedback loops are encouraging, and make it easier to build momentum. I hate being deep in a problem then having to "wait" for a compile.
But compile times have a massive effect on developer time, which has a massive effect on the productivity and the amount of work that can actually be done.
Comparing compile time to run time is rather strange, but compared as a percentage of a developer’s time, it’s very obvious why people are worried about it.
I think it's a bit of a shadow argument.
So for business, the logic goes:
Goal := save(Money).
time(Developer) := costs(Money).
Therefore, to achieve our Goal, we optimise developer time.
But more often than not, businesses don't know how their developers spend their time. So as such, they optimise for results. The business doesn't care how you spend your time, as long as by the end of Sprint/Deadline/Whatever you have a result and/or a reason why not. And I'd bet some money that the reason will very rarely be "my compiler took to long".
From a developer standpoint, I understand better (mainly because I'm a developer). But it still lacks a bit: So I started using Rust and I have a long history with C. The first compile with Rust takes very long (because of loading all dependencies), but afterwards it is slower than C, but it's okay. In return you get a lot of extra safety for your program, it's basically time you spent on your C program to fix all those nitty gritty memory safe optimisations and making sure there's no dangling pointers and free(NULL) errors. Of course with experience, these get less and less, but there's always risk. Nobody is perfect.
For me as a developer, it's more of a shift in my thinking - which is, to be fair, hard to enforce on people and can only come from oneself. But now that I have a compiler which supports me handling memory and pointers, my mind is more at ease. It does these things I spend time debugging on for me (most of them, not all) and in return for longer compile time, I save development/debugging time. At first it feels a bit less productive, since you are just sitting around watching your compilation (there's an XKCD for that https://xkcd.com/303/), but you could also spend this time writing documentation, reading up on something or just grabbing your coffee (or leave the office and check in tomorrow). Things you would do anyways, it's just a matter of how you mentally approach it.
I think the downside only comes when you want it to be negative, or when you're still transitioning.
For the lifetime of a binary, compilation time is like 0.000001% of its existence.
I’m more than happy to wait longer compared to other languages (even zero time at all with scripting languages) while cargo does it’s thing.