Using date stamp down to milliseconds / ticks as a salt?
You're going out of your way to create more work for yourself, and introducing a vulnerability. It's not necessarily a huge vulnerability, but why bother?

To get a number string down to the millisecond - If you can guarantee that you'd not have two requests in the same millisecond.

You cannot have such a guarantee, not without doing very complicated things.

If your server is fast enough, it may take less than one millisecond to serve a request. Even if it doesn't now, maybe it will after a hardware upgrade.
Clocks are not always accurate. Just because you have a function GetCurrentTimeInMilliseconds() doesn't mean that it has millisecond accuracy.
The time can go backward if the clock is adjusted. Or if you use the local time rather than wall-clock time.
If you have multiple threads running on multiple processors, they will, from time to time, happen to serve a request at exactly the same time, no matter how much resolution your clock has.
If the same code is running on multiple servers, it's the same thing: they'll all be generating the same number at the same time.

Depending on the purpose of the salt, repeating a value may or may not be catastrophic. For a nonce or IV in encryption, it is often catastrophic. For password hashing, the attacker only has a small advantage if the salt is rarely repeated.

then go and prepend it to the saved hash - right? Otherwise, I can never check the hash against a known input.

Yes. This applies no matter how you generated the salt.

So making a super strong salt, with crazy random entropy to then go and store it right next to the data it's salted makes me think, is this wasted effort? Or theatre to seem great but really all you need is a unique piece of data to provide the salt?

You don't need “crazy random entropy”. You just call GenSecureRandom() or whatever your function to generate cryptographically secure random bytes is called. This is less complicated than the date-based approach you propose!
Even better, when hashing a password, the password hashing library should take care of generating the salt. But if you're stuck with an old API that requires you to do the work, then just generate a random salt of the length stated in the documentation of the library or of the password hashing algorithm. This is the simplest method.