I still use the strap on steps on public land but use the screw-in steps on private land when needed. But I definitely prefer the safety of a ladder stand. Sticks are nice too.

So I guess, if I had to do it on a limited budget, I would not have a problem with screw-in steps on private land in trees that have no value with the permission of the landowner

As far as safety of them, I have never fallen or had one come out of the tree and I have been using them for 25+ years. Always check them and take responsibility for your own safety. They do kinda suck with muddy or wet boots, climbing down in the dark. Take your time, use a light and a static line with your harness. Also, anticipate where your nuts (I assume you have nuts but the other option would be no fun either I would guess) are gonna be if you fall and make sure there isn't a step there.