Is SWD with an FTDI chip a universal programmer solution?
The ARM SWD interface is 'generic' in that the interface protocol doesn't care about the target hardware. So assuming that your programming device operates at the right voltage, yes, it can work with any hardware.

Behind the SWD interface, the registers which control debug in the SoC are memory mapped. Although these are standardised in a sense, for any debug toolchain there will often be a degree of customisation required (at the software side). For example, a new CPU will have a new ID code value, and maybe some additional architected control registers.

You basically have the choice of implementing the SWD protocol in software on your PC, and using a USB-to-pins interface, or implementing the protocol in a micro-controller and presenting a USB endpoint which 'does debug'. Doing the latter is what almost all of the dev-boards with a built-in debug interface do, along the lines of SWDAP and the DAPLink software. Often these dev boards are configured so you can break-out the SWD signals and use them to debug your own target hardware in an end product design.

If you chose not to implement DAPLink, you might be more limited in the toolchains which support your interface.

In the past, the SWD protocol documentation has been complicated to get access to, and this seems to have let to a degree of confusion when it comes to generic probes. The old pre-CoreSight JTAG interfaces were also much more device specific, with a TAP controller implemented within the CPU.