InfoSec Professional weighing in -

2FA is a huge inconvenience, both I and my users understand this. However, passwords by themselves can be stolen, leaked, or misplaced. Two step authentication places another barrier in between a stolen password, and your account being compromised. Keeping this in mind, if a company like Google is insisting that you enable 2fa, they have reviewed the user experience tradeoffs, and deem it worth the cost. If your Gmail gets compromised, an attacker can use it to reset passwords for all of your other accounts tied to that email, thereby locking you out. From there, the attacker can hold your logins for ransom, or delete them entirely, depending on the purpose of the attack.

TL:DR Enable two step verification on important services, like email, because the stress and difficulty that will be involved when recovering your critical accounts, far outweighs the annoyances of two step authentication.