I think it depends. If you have just one kid, and are SAHM, for us there were just no situations when I was farther than one room from him, in constant vocal or hearing contact and would hear right away, if not witness any bathroom blunders. So we never did any bathroom safety. The whole no-substitute-for-supervision thing.
On the other hand, if you have more than one kid, or aren't the sole/main caregiver, or have many things pulling your attention in different directions, it might make more sense to have only adult-supervised toilet visits.
"That's the way it is, if that's the way it seems to you."
"Cosi e se vi pare."
We've always had an open door bathroom policy. We keep the lid down and tp and cleaners out of reach (he LOVES toilet paper). He is old enough to lift the lid, so we do more hand washing these days (he only splashed in there once, but ick). He is my first kid to touch the water, actually.
I have never encouraged potty dumping by young toddlers and all my kids used the toilet before I thought I wanted them to carry around a sloshy potty (ick).
ETA: I couldn't find recent statistics. It looks like an average of 4 drowning deaths per year in the late 90s. 2 in 2002. I hope I'm not sticking my head in the sand on this one, but low flow toilets started replacing the big guys in the mid 90s. While it was rare before, the water level dropped with the low flow toilets, so it's not nearly as deep as it once was.
All that said, if you have a toilet seat adapter locked on the seat, can he even access the water? I didn't think my older kids could lift the seat or reach through the hole with the bjorn.
To be clear, he doesn't get to carry the dirty potty. He just gets to walk with us and help us dump and flush.
You had your bjorn seat reducer locked on the seat? So it just stayed there permanently? Ours hangs on the side and we just put it on when he is using the toilet.
We tightened it as tight as it would go and the toddlers couldn't get it off. I don't know if they tried hard. I thought it made a fine toilet seat when I didn't feel like lifting it off. I do tend to think kids who use the toilet are less interested in it.