There are at least two benefits to integrating the controller into the M1 SoC. (Note, the NAND is not integrated. More on that in a bit.)
One is that Apple doesn't need an extra DRAM chip just for the SSD. They just set aside some main DRAM. This is possible because the controller is just another node on the SoC's internal NoC (network-on-chip); it has full access (at very high speed) to system DRAM.
The second is extremely high security. Secrets needed to read and write the flash media can be kept entirely inside highly secure parts of the SoC which are designed to provide no path for rogue software to read from. When the disk encryption key is created, it's randomly generated by the Secure Enclave TRNG, and is never allowed to truly leave the SE. When it's in use, the key is only available to a hardware encryption/decryption block whose only outside interfaces are encrypted data in / decrypted out (or vice versa).
Thanks to this unique architecture, properly configured M-series Macs are extremely resistant to attackers who want to extract data from the computer without your cooperation, even if the attacker has physical possession of the machine. The same cannot be said of Windows laptops, even with Bitlocker. Does this matter to you? Probably not. But it's been a major focus for Apple over the past decade. They have delivered the highest level of security currently available in mass market personal computing devices. Part of it is enabled by this tight integration between the Secure Enclave and SSD controller.
Finally, the NAND. I mentioned it isn't integrated. That's why it's able to be on removable modules in some AS (and T2) Macs. The interface between Apple Silicon SoCs and NAND memory is, of all things, PCIe. Since nobody actually makes NAND flash with a direct PCIe interface, Apple designs these little interface chips which speak various NAND flash protocols on one side and PCIe on the other. Note, these are not anything like full SSD controllers, they're a very low level abstraction over raw NAND.
Does that mean anyone can make proper NAND modules for AS Macs? Nope, the protocol is completely undocumented. While it's certainly plausible that it could be reverse engineered, an important barrier is that the system design downloads a firmware image unique to the NAND manufacturer and flash generation, these firmware images have to be signed by Apple, they're designed to execute on these Apple-designed interface chips (each of which contains an Apple designed embedded Arm core, btw), and Apple put all this together for their own convenience rather than flexibility. So there's lots of ways to have it fail to work if the interface chips aren't Apple's and/or the configuration isn't exactly something Apple has already shipped.