1) I'm pretty baffled by "text message should be used only for time-sensitive communication." There's absolutely no "correct" way to use text messaging, I don't use them for time sensitive communication, I treat text messages the opposite way, I'll get to my text messages when I get to them. If you want my attention now, call. I am not alone in this considering half the time I send a text in the morning I don't get a response until the afternoon. I actually anticipate this since I [naïvely?] assume people are actually working while at work. For me, I'll check my notifications at work when I get up to go to the bathroom or get coffee.
2) [Almost?] all companies let you opt out of text message notifications and/or customize it, I've never seen a company that didn't. For example, for Verizon I just go into "Manage your communications and alerts" online and set it to "email" rather than "text." Phone companies set text by default only because they already have your phone number.
3) Assuming you don't have a dumb phone, this is a solved problem, just put your phone on "do not disturb" while you are working. You can set it to where priority numbers (like your spouse) still give you notifications for emergencies. You can even set "do not disturb" to automatically coincide with your calendar events and/or time of day.