The short lesson:
A relay is a piece of digital equipment in disguise. Yes, it's digital in that it has only two states: the contacts are either open or closed. No variability allowed.
The slightly longer lesson:
A relay takes a low-voltage input and uses that to control something. Originally that would've been a high voltage of some sort, but it can be anything. An example might be your garage door opener - the button on the wall is very low voltage, but it controls a high-voltage motor (by that I mean house current, of course).
Now, putting all that together, and in context......
A relay can't do anything for us except to include or exclude an effect from our signal chain. Whether that's a bypass function or some other method of control, that's the bottom line - we hear it, or we don't.
Now from that we see that a relay isn't really necessary, we can simply run a pair of cables out to a foot switch on the floor. But if those cables are carrying our signal, then we're adding lots of cable capacitance, and we all know what that means, right?
So even here, a relay can help - we can use a non-signal cable to control the signal path. That means, the actual signal patch cords are quite short, which is a good thing.
Now, using such 'remote' footswitches.... yes, that could mean a bundle of individual cables. But consider - the control voltage is what actuates the relay, and you can buy units that will operate on as low as 3 volts DC, and at 150 to 200 mA of current. That means a 22 or 24 gauge wire can handle the job just fine. And such "tiny" wires can be found in already-made bundles of 5, 8, or 10 pairs, even more if you shop around. That's a lot of control capacity in one jacket (the material covering the wire bundle).
All things considered, the only drawback to using several FS-6's is that each of them must have a battery installed, there's no getting around that. But I've had a battery last as long as 8 months, if I remember to unplug the cables before I pack it in for the night.
Make no mistake here, MIDI can do the job, but keep in mind that there's a start-up cost in terms of dollars, even when you buy used. And there's a significant learning curve that can be only partially bypassed by asking questions in a forum - you simply have to get your hands dirty, there's no magic bullet.
However, there is one way you can experiment on the cheap. Find and download a free program called MIDI-ox. This thing monitors your MIDI ports, and reports on screen just what signals are coming in, or it can send out whatever you wish, right from your keyboard. It's a very comprehensive package, but at the same time, it's simple as all get-out.
Now go out and procure a Behringer V-Amp of some sort, or perhaps a Line-6 POD. Most PODs are MIDI-capable, the V-Amp equipment always is - that's just the way they roll. Your local craigslist probably has at least one such up for grabs, and most likely for not much more than your next round of drinks with your mates. When you're well up on the learning curve, you can either keep it, or re-craigslist it back out.
If all of this hasn't phased you, only whetted your appetite, then you're ready for a Behringer FCB-1010. Even new these things are less than half the cost of comparable units, but they're built like tanks, and if you get into them in a serious way, there's a software editor for your 'puter (Windows, Mac and Linux versions are out there) that will make modifying patches oh-so-easy.
Still, none of this has addressed the real issue, that of controlling one or more effects units. That's gonna cost ya, sorry to say. It's like there's a sign hanging on our foreheads: "I have money to burn, and I wanna give it all to you for one lousy stinkin' piece of cheap-butt gear". Apparently MIDI manufacturers live in a different world than us musicians....
Your whole project is doable, but you need to decide - price, ease of use, reliability, expandability (ash's concern), all of these factors must be considered before you jump in the pool, or your wallet is gonna bust a cap in yo butt.
One last thing:
You expressed a desire to be able to run every effect's input and output jacks to a panel on the back (or was that the front?), and there you could simply swap short patch cords around to alter the signal chain. That idea is called, amazingly enough, a patch bay. They can be found in various physical dimensions, I don't know if they're available for rack-mount setups, but it wouldn't hurt to look. But here again, a set of relays can do this for you, if you want to ratchet things up a notch......
HTH
sumgai