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.
EDIT:
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.