This is fundamentally tricky because email has so much more functionality than SMS but let’s say the email can be limited to
text/plain and the content length to “short” (and limited to who-knows-what regarding character set 1) …
The first question I would ask is whether the actual mobile service provider that Purism is using for AweSIM already offers this. Don’t want to reinvent the wheel. Right?
If not, then while this is relatively straightforward to set up (with a range of either product or service offerings already in the market), it is not zero cost. So the obvious question would be: who wants to pay for it?
There are always complications. For example, you probably want to put in place measures to avoid misuse (spam, high volumes). (SMS is fundamentally bad in that regard because there is no such thing as an unguessable mobile phone number.)
Perhaps you should be hassling the FCC to allow SMS as an alternative to email. That way no gateway would be needed. Perhaps if you could get an answer from the FCC on that, that would immediately indicate why email-to-SMS won’t be viable for their purposes e.g. they are going to send you multi-megabyte PDF attachments, …
So maybe what you really want is a mailbox that sends you an SMS notification when the mailbox receives something - but that is of a slightly different nature compared to what you appeared to be suggesting originally.
If you are a Librem 5 customer then there are probably other ways of achieving this, that don’t involve ongoing cost and don’t involve using the SMS functionality at all. After all, the essence of secure communication is to move away from anything using vanilla phone network functionality, whether that’s calls or texts. Once you have secure communication via the internet, perhaps your email service provider (is that Purism???) can bridge that directly into some secure communication platform - and that might apply even without a Librem 5.
So maybe you could also ask the FCC to support secure messaging platforms. LOL. Regardless, you could perhaps indicate whether you are willing to use a secure messaging platform instead of SMS.
1 It is acknowledged that AweSIM is US-only at the moment, so character set can presumably be ASCII and not something to worry about but I suppose Purism would at least have on their radar offering AweSIM in other countries where character set would be a consideration.