I keep getting prompts to 'upgrade' my account security to use 2 factor authentication.
The reason I am hesitating using my real phone number for unlocking my devices is because I don't want to be in a situation when I am traveling internationally and am unable to unlock my computer.
So far it seems I have only a few options :
Get another Apple device, like an iPhone SE or the base model iPad, for the sole purpose of unlocking my account and take it with me everywhere I go internationally.
Use a Google voice number which I could associate with a local number while travelling, to help me receive a 'roaming SMS'.
If I can figure out a reasonable solution to this, I may consider changing the security settings.
I wish Apple would just provide an app based authenticator like Google and Microsoft.
It seems from the answers and comments that
computer accounts and
iCloud (online) accounts are kept separate despite the push for 2 factor authentication.
This is really encouraging, but I will do some more research on the changes before switching.