Aftermarket Speakers

Componets will be your best bet. The mach system works really well when paired with the right speakers. Just adding a speaker that isn't matched with the factory amps results in less than desirable results as described.

Are the Mach 460 speakers considered components? Can the speakers themselves just be replaced without any other modifications? What about the subwoofers?

They are not in the sense that you're thinking.

How I've done it in the past (when not running an independent aftermarket amp). Run a nice 5 1/4 or 6.5 component set up front. Use the door speaker as the feed for the crossover and it gets a full range to handle tweets and mids. The rear deck can just be replaced with a nice 5x7/6x8 3 way speaker. You can run 2 way's if you have a head unit that can pre filter the frequency and you have actual sub's to make up the low end of the spectrum.

As with stereo's there are a million different schools of thought and ways to do it. If you're wanting a good upgrade then components and aftermarket amps are the way to do it but it turns into a lot of work and can get pricey.

To cover all the bases I would recommend:https://www.crutchfield.com/S-mwtA9TOMsaG/
Their tech's really helped me out with mine(after the previous owner screwed it up and sounded like it was underwater) and I didn't even have their parts!

The best quality and easiest way to go, as well as most expensive, is to throw all the factory junk in the garbage can. From there, you run an aftermarket head unit to an amp or amps, run components in the front, delete the rears, and throw a sub somewhere, most likely the trunk.

The sound quality in a Mustang is going to suck regardless though. Between the road noise, creaks, and rattles, you can't get excellent sound. I'm bypassing my Mach 460 stuff and just running four mid-tier speakers off an aftermarket head unit. It's so noisy headed down the road that it doesn't matter. The flip side of that is my pickup. It is very quiet so I didn't feel bad about stuffing $3-4k worth of audio in it. I don't think it's worth it with a Mustang.