Randomizing RAM is more accurate because it makes the RAM content unpredictable, which is far better than initializing it to a set value. The values in unitialized RAM depends on types of RAM chips, temperature and probably many other kinds of things related to physics, so it is very unpredictable and very hard to simulate accurately.
Yes it would be a great feature if a flahscart could boot a game directly without having to pass a menu. Besides solving any initialization problems it would also solve problems like Super Game Boy 2 linking (works a bit different from other Game Boys), GBA-GC linking (for some games that expects a certain cartridge), N64 Transfer Pak, GBA-NDS linking (inserting a GBA cartridge in slot 2 of a DS, linking with a DS game) etc.
The only Everdrives that allows bypassing the menu are those that use flash, if flashed with a game then booting without the SD card. But even those seems to load some kind of bootloader first that checks for the SD-card, so those don't count.
Some flashcarts that do allow bypassing the menu are: GB USB 64M Smart Card if only one game is flashed to it the menu program will not be flashed (although this flashcart is pretty low quality and has many other problems), and FDSStick this one also doesn't flash the menu program if only one game is flashed to it. I guess any simple menuless flashcart like Flashboy+ that just flashes the game to flash ROM also don't have this problem.