If all sats have equal value, would you willingly switch your current onchain sats for sats obtained through mixers, and then try to deposit the new sats at a reputable centralized exchange?

If they had the same value - if they were truly fungible - then it wouldn't matter, and indeed, nobody would even be able to tell that this operation had been performed.

All sats *should* have equal value, but because Bitcoin privacy is dodgy at best (and yes, I am aware of all the workarounds and employ them myself), they don't - in every situation, but at present only in certain ways will that become a problem (most notably with CEX, which are bound to obey the law, which is employed to maintain pervasive financial surveillance of everyone, with no regard for the presumption of innocence).

Simply put, the pseudonymous nature of Bitcoin is not enough to enable fungibility. All sats have a history, if you try to erase their history, that becomes their new history.

Now if you ask me if that should matter - no, it shouldn't (but makes for a clumsy solution for financial privacy). But it does, and it is a weak point, and being a weak point it is being leveraged by entities hostile to freedom and self-sovereignty, and it will probably get worse before it gets better.