EDIT: With all of that being said, since you're someone that apparently used burned discs, I must ask - within the last 7 or so years, has there been any benefit to burning optical discs rather than using a USB loader? (not counting warm fuzzies from physically inserting a disc into a game console... which isn't really something I know about anyway since I grew up with cartridges on consoles and discs on PC, and the GameCube was top-loading with small discs and therefore "feels" very different; the GameCube and Wii are the only disc-based consoles I own, and I guess a PS4 that a friend is perpetually loaning to me)
Thing is, being quite the hardware computer geek (not software - I can't code worth a darn!) that tends to get all of my friends and relative's older PC parts through the motto of "don't throw it away, throw it my way!", I'm kind of spoiled for choice when it comes to spare 2.5" SATA drives that I have just laying around unused, so all it took was a known-working $10 USB-SATA adapter and I was set to use whatever drive I wanted (...though not before I went through like 6 different USB flash drives of extremely hit-and-miss compatibility which is actually why I bit the bullet and went the USB-SATA adapter route instead which "just worked" first try).
Oh I never really hardmodded any of the consoles since the Wii and onwards, they've all been softmodded on my end.
The burned disks stuff was possible thanks to modified IOS on the Wii side (the famous CIOS). That's how I recall doing it
As for your question on the possible benefits of running the burned disk, possibly two:
1) Recreation ISO with Other M "Redux" already burned into i.
2) Burning the original Other M ISO, the Wii might read it as an original disk and this could allow for an easy way to side load with Riivolution... maybe? Without the hassle of making the ISO from scratch with all the mods patched in.