If you don't want to experience this SMS verification issue as I said above better switch on any authenticator app. SMS verification is very problematic not only on exchanges but also on some other websites.
Yes, switching to google authenticator is much better option but why don't exchanges offer two 2fa methods at the same time. For example, if there is a option to use either SMS 2fa or google authenticator at the same time, so if one is not available , the person can login with other one
That would be very convenient but you'd be sacrificing your security in exchange.
Different method = different attack surface which means some offers better security than the other and this would be meaningless if it's also possible to generate an OTP thru a weaker point as hackers would target that instead, just like how it is with your example as software/app-based authentication offers better security than SMS-based.