When you send an SMS text message, there's a understanding (and therefore, an expectation) that it goes directly to the recipient's phone/smartwatch and that they can reply immediately; i.e.: it's a system for high-priority (and therefore highly-intrusive) communications - this is why people generally don't give-out their mobile-phone number to strangers.

Unless you go to the effort to tell people that you route your SMS messages to e-mail and therefore reply in-your-own-time (hours/days/weeks delay), the people trying to contact you aren't going to expect that: they're going to expect you to reply much sooner. I'd be out of a job if my boss' panicked SMS messages about how our prod website is down went to email instead of my phone.

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Any kind of "universal" messaging platform that anyone can use to send anyone a message needs to allow recipients to set how maximially intrusive those messages are - but senders might also want a way to set how minimally intrusive those messages are. Those requirements cannot be easily reconciled in a way that protects privacy and prevents abuse while also allowing anonymous and unsolicited messages or senders. So far the "best" way to do that today is by segregating senders (not recipients) by system (e.g. private SMS for high-intrusive; less-private-but-guarded e-mail for low-intrusive; public social-media, etc).

Consider services that tried to work-around that, such as LinkedIn's paid messaging feature - which didn't exactly go very well.