Is 0603 vs 0402 assembly mass production cost optimization still relevant?
Many assembly houses these days do 0402 with the same machines they do anything else, possibly using a different needle, though I'd suspect they'd be using the 0402 capable needle for 0603 and 0805 as well.

Is it still true you'll have more choices when you don't go below 0603? Sure. Most likely. There's a lot of cheap assembly houses that are cheap because they use the old equipment of the others, probably everywhere around the world. Some assembly houses may do down to 0201, but not be too happy to do the smaller stuff, because it requires extra operator attention.

However, when you go into volume, the cost of the more advanced assembly house will likely not weigh up to the cost difference for smaller circuit boards, more efficient systems and/or lower component cost. And some times using 0402 or even 0201 offers better per-component performance as well, such as lower parasitic effects.

Obviously if a 5000 unit reel of 0603 capacitors costs $15 and the 10000 unit reel of 0402 of the same value cost $20, that'll add up when you're making 10's of thousands with 10 each, but not really do much at all below using a reel per month.

Because boards are now almost always made to 5mil/5mil standard, the board won't likely be much more expensive if you make anything more compact with tiny components, but at high volumes the board space savings will start weighing as well. If a panel costs $100 and with 0603 the panel can fit 20 PCBs, but with 0402 it can fit 25 PCBs, that usually saves much more in volume than any extra cost you have at assembly in high quantities.

In all, if you want to be fully sure you'd need to do a cost estimation, including an RFQ to a few assembly houses that tickle your fancy. All the assembly/full-service houses I use are always ready to pick up the phone or answer an e-mail with questions about comparative costs. And more often than not I find the cost increase of something "unwise" 10 years ago falls into the less than a few percent now. And the same will happen later to stuff we think expensive now, so, really, you need to regularly keep asking them if things have changed if you want to be the best designer you can be.

Summarising: The only reason I don't do at least 0402 in my designs is if it's a hobby thing for me or others, where I want to be as quick as possible with replacing components, or I want others to be able to use my design as well, as I am not even noticing significant cost increase up to 160mmx160mm boards at 10 units. Over average past orders.