Yes, but …
You get an email address that serves as a “gateway” to the SMS system for delivery. So the mobile user receives it as a text message. Which means among other things the “subject” field and the rest of the email header info is lost.
And now you have a convo proceeding in two comm channels. The recipient can’t directly text back since there’s no phone number associated with the email when it arrived at the gateway. As mobile devices have gotten more “computery”, it becomes easy enough for the gateway to include the sending email which the recipient sees in their SMS app as a clickable “mailto:…” link that, when tapped, fires their email client to compose a reply.
But back in the early days where SMS was a carrier function and any browser or email was a 3rd party function, not so much. App-to-app integration or even communication was anathema at that time. Or on T9 devices from the pre-“smartphone” era.
So in a sense, the SMS can serve as a call on “the hailing frequency” to begin an email conversation on the “working frequency”. At least nowadays.
There’s another big irritant from the sender’s POV. Which is the topic of this thread. Given the 10 digit phone number there is no directory anyone or any app can consult that reliably maps the phone number to the corresponding email->SMS gateway address.
At one time back around the turn of the century (golly that sounds quaint, almost Edwardian) I was responsible for maintaining a system for mass-blast SMS. Back then there were literally hundreds of mobile service providers in the USA. Each with a distinct gateway domain name. Obviously long-tail applies, and the then Big 5 carriers covered 80+% of the users. But this was public-facing and had to cater for “100%” of users, or so the BizCritters told us.
Due to the still-regional nature of mobile carriers back then, any given state or region would have it’s 2 or 3 “big” small carriers. Which would be completely absent 4 states away who in turn would have their own big smalls.
And darn few Americans even today know this feature exists, so if you ask an end-user to supply the email->SMS gateway address of their mobile phone they simply respond “huh?” Which is what drove us to have to know every mobile carrier in the land so we could ask the 2-part question: 1) What is your mobile number? and 2) Who is your cellular carrier? Most users could get that right. Mostly.
And of course the cellular carriers were constantly going into and out of business, merging, renaming themselves, etc. Which constantly invalidated our table of carriers and the domain name stored for any given carrier.
Once mobile subscriber number portability came in, then end users could move carriers. Which didn’t change their mobile number but did change their gateway domain name. Our market was B2B, B2G, & G2B where you would think you’d have a more disciplined conscientious userbase who’d tell us these things, or at least notice when the flow of email->SMS messages dried up, usually just after they got a new phone. Well, we thought wrong about that too.
But yeah, there is an email address associated with every mobile in the USA. And because of our receiver-pays culture, there’s a disclaimer on every website asking for this info, or simply the mobile number alone:
We might send you an SMS. If we do that, your carrier might charge you money for that. That’s your fault, not ours. It’s your responsibility to pay them without whining. Click [OK] to agree.
Bottom line, it’s the usual USA cock-up where the idea was thought through about 10% of the way, released into the wild, then all the harder, less shiny parts were ignored in the name of greater short term profit at massive longer term hassle and cost.