The thing I find odd about sms 2fa is I sometimes get multiple services texting me through the same short code. Isn't that a security hole in itself? If a user recognizes a number as the "security number that texts me sometimes" and I as an attacker know this, couldn't I somehow abuse this?

For example: "Please go to x url and enter your password" -> user enters pw -> show new form with 2fa code input (and in the background, try logging into their account with the pw supplied) -> user gets another text from the same number, enters in your site -> profit???