But you're describing a fairly complicated scenario where you have multiple public API's with different request types, internal data (hopefully canonicalized at the border) and response types.
How do you keep track of all that data conversion without types?
On my last large project, I had to wait 10 to 15 seconds for the code to build every time I saved the file (and yes the compilation step was optimized to only include relevant code; a large number of dependencies don't help).
So every time I made a change to the code to check something, I had to wait... You can't use console.log() to quickly check stuff anymore; the compile overhead is so significant that you're forced to pull up the debugger and manually step through the relevant code every single time you want to check something (you want to get as much info as possible from each debug cycle because it's so slow).
When writing plain JavaScript, I only pull up the debugger when it's a particularly difficult bug (e.g. a race condition). For most bugs, I can get all the information I need with just a couple of calls to console.log() in my code. The debugger is just unwieldy.
The case you describe very rarely happens to me with JavaScript; having fewer primitives to work with greatly reduces these kinds of issues... Sure it opens up the possibility that you'll do something stupid like trying to add an object with a string; but that's a pretty silly thing to do. If you name your variables properly then that never happens.
With C/C++, there are many primitives so you might get errors when you try to assign an int64 to an int8 (for example)... With JS, however, because there are fewer primitives so the odds of that happening are much much smaller.
Because there are so few primitives in JS, it's easy to remember how they all interact with each other. The only exception is the boolean truth table for '==' (which is a mess); that's why it's usually recommended to use '===' instead.