Well, not necessarily. You can reconstruct a multi-sig wallet on anywhere between 1 and m devices; it's just safer not to do it all on a single device.

There's certainly nothing stopping you, but I guess you would have to weigh the risks of making a mistake writing down a Base58 master public key, versus the risks of incorrectly transcribing your Base58 key to a phrase and doing something non-standard which would be more difficult to recover from. I'd prefer the first option with meticulous double checking - write it down in Base58, double check it, and then recover from your written down key and check it all matches up.