That is one thing they do quite well. I've not found a good analog for day-one sparring for my students. We don't do ground work that early, so no rolling at that point. They can't take falls from throws yet, so no standing grappling, and besides, they wouldn't know the throws yet. The strikes they learn early are knees and elbows, and the first block is the "plow", so striking grappling would be problematic. Our early physical instruction is focused on teaching them a few escapes, a few simple techniques (the elbows and knees and plow), and starting them on basics of movement. The closest analog is that they get to fairly quickly accept an attack and give a response - a bit of one-step sparring, perhaps.BJJ does one thing I fear many clubs stopped doing or never did in the first place.
They do rolling/sparring from day one or near enough. It is something they have the possibility of doing.
Some clubs around where I live consider sparring to be competition and to be avoided until you are experienced and trained enough. Now in BJJ you learn from that rolling, realizing that there are always weaknesses in your movements even when you think you got it down well enough. No mystery, just teaching you that learning a technique means more than just doing it over and over in a drill.
I have been working on moving sparring earlier, and even randori ("sparring" for standing grappling) though that's always going to be a bit later, but I've not found a good way to bring it into the first few weeks.