It will bring the prices down somewhat because the game would be more available. A big reason that you see some of these games at high prices is because these games are locked on old hardware, and they cannot be played on modern consoles. Look at
Super Mario Sunshine. The prices for that game almost cut in half after Super Mario 3D All-Stars Collection released.
Goldeneye saw a similar drop earlier this year. We already saw it with
Metroid Prime dropping 33% since the Switch version launched. Availability is a big driver in the market.
Now it isn't an exact science by any means.
Earthbound has been readily available on the last three Nintendo systems, but that price has only gone up. To be fair though, Super Nintendo has that aura around it that will always keep prices high unless a massive crash happens. Even then though, I think SNES collections will probably hold their value until the end of time. That system probably carries more nostalgia than any other system. Pretty much any title that isn't a sports game will garner at least $15~$20 these days.
Ok, SNES rant is over. Bottom line, yes the Gamecube prices will come down. They won't crater, but I wouldn't be surprised if they came back to the $50~60 range.