When should bare die be used instead of QFN/BGA packages?
Asking pros and cons of Bare dice vs packaged parts is like asking the pros and cons of buying a house versus flying an airplane... The circumstances where a bare die is appropriate are very different from PCB design. This is really a design project for a certified Professional Engineer, not an internet Q&amp;A. There are legal and ethical obligations as well as mechanical and materials engineering challenges involved in designing something sold as an IC or as a SoC (System On Chip).
Bare die on PCB is sometimes used on consumer goods in high volume, but there are steep setup costs. See for example this question about Chip-on-board assembly: What is the Chip-on-board ic used in calculator, how to obtain one and how to use it? and see also this tutorial from sparkfun: https://learn.sparkfun.com/tutorials/how-chip-on-boards-are-made  -- Would not even consider unless you are a big manufacturer with an established relationship with an IC fab house or IC vendor (in which case you wouldn't be asking here). I don't know of any distributors that stock dice.
Dice sales for custom hybrid packages might make more sense (you mentioned a System On Chip as a design goal), but still requires a close relationship with the chip vendor.
Bonding a bare die to another substrate is usually done with some kind of epoxy -- conductive or non-conductive matters. So does the temperature coefficient of the substrate. And wire bonding (welding) from die to leadframe or from die to PCB requires special wire bonding equipment. It's not a normal step for a PCB assembly house, but would more likely be done by a hybrid assembler. Bond wires are not insulated, so it's important that the dice are installed with the correct orientation angle (not necessarily on a square grid) to avoid crossing bond wires. I've seen this on some of our stacked-die products (which look just like ordinary ICs from outside).
If your company's goal is to make a System on Chip, then isn't the idea to end up with a chip? That's a very different skill set than PCB design. Designing an IC package (or a hybrid SoC) is much more demanding of mechanical engineering / materials engineering skills than PCB design. There are also more stringent legal/testing requirements... you may run into nasty surprises when using a package-inside-a-package, like failing humidity/temperature test characterization.
If you need to be able to support the product in the long term (i.e. will not be obsolete after 1 year), you will need to consider developing second sources in case one of your component vendors drops a product you need. This happens pretty often with memory chips, as the memory sector periodically updates their production capabilities.
My company (one of the major analog chip vendors) does offer dice sales, and it's not generally advertised on the internet. You would have to have an actual conversation with someone in sales, as a start. You might also have to enter into legal NDA / sales contracts at some point. As a hint, you should start from what actual IC function you are trying to buy, in what volume and timeframe, and then contact a human being in sales, applications, or business management, and ask them whether they could offer that product to you in bare dice form. (BTW &quot;die&quot; is the singular, &quot;dice&quot; is the plural.)
(Not mentioning my company's name because this is not an advertisement or an offer of goods or services. If you need one of our parts you'll find us. Just giving some background information.)