The 386SX could do everything the 386DX did, just slower. My first Linux box was a 386SX machine. Before Linux, I ran Coherent on it: https://en.wikipedia.org/wiki/Coherent_(operating_system)
I paid $99 for Coherent because Linux didn't support the fancy RLL hard drive in my work computer. Eventually Linux caught up (or I got a new computer) and Slackware replaced Coherent (for little things like X11, better networking etc.). Those were the days :)
I had a 386DX, 25 MHz with 4MB and ran Slackware 3.0 with kernel 1.2.13 on it. It worked pretty nicely for me, but I have to say that I spent most of my time on the console. X11 did run but it was too slow to be fun.
Once Linux stabilized, the writing was on the wall...