The really clever step for pirate modders would be to add to modded consoles full internet connectivity without going through Live.

^ suprised no one has done this actually

I consider not having access to XBL a big deal. Even if you are a silver member and do not care about playing online at all, you get access to DLC (some of which is actually free and awesome), XBLA games (all of which have free demos), free demos for a lot of retail games (since you are legit, this is a nice bonus for you. The pirates can always pirate games if they want a demo). You also get game patches (lots of games ship out buggy this gen so this is very important). You also lose HDD install functionality when you get banned btw (HDD installs means less laser wear, less chance of disc wear, less heat generated by console, less noise).

For pirates to sacrifice XBL just so that they can play games for free, it's totally not worth it. They are settling for an upscaled last gen experience (in fact worse than last gen in some ways as games ship out buggy these days whereas last gen devs weren't as lazy because there were no patches to fix mistakes) as opposed to a current gen experience.

Piracy is pretty tempting but you know what? I can't imagine going back to piracy because it's difficult enough for me to keep up with backlogs with legally-purchased games as is. Back when I used to pirate a lot, I had tons of burned CD-Rs and DVD-Rs that would just lie around unused. Video games are actually very cheap forms of entertainment. I have like 14 360 games (15 soon) and I'll be buying more definitely and yet I haven't come anywhere close from getting my fill of the games I currently own.

You are wrong. Modded (or to be more precise flashed) consoles cannot play games from all regions, only from region of origin. If you have for example PAL console, you can play PAL and region free games, but not NTSC (both US and Japan).

Modded XBox 360 banned from XBox Live is a small price to pay considering on the savings you would make from downloading pirated games to play on your modded XBox 360.

It isn't just a ban from Live, it also does this as well:

Why does my banned Xbox 360 no longer install to hard drive?
Once a console has been banned from Xbox LIVE, in order to protect the integrity of the Xbox ecosystem and its members, that console loses its ability to create trusted content.  This means that, for example, the console can no longer create profile and game data that is recognized by other Xbox 360 consoles or on the Xbox Live service, and it cannot create trusted game files or recognize previously created game files using the install to hard drive functionality.  The inability to create trusted content does not impact the console’s ability to play from discs in the optical disc drive.

http://www.xbox.com/en-US/consoleban

So long as the XBox 360 can still play games on it that is all that matters. So do not bother playing games that require game saves.

I thought an XBox Live ban would just stop you from playing online or using XBox Live on the banned XBox 360.

Some people who have both consoles play online on PS3 and pirate games on Xbox.

Maybe with a memory card or the integrated memory on the newer systems ?

You can save on HDD, even if you have banned console. But, when, or if, you buy new console, you cannot transfer such saves and profile. If I put it simply, whatewer is on banned console can be used only on this banned console.